# The size of the radius of the event horizon of a black hole created by the merger of a black hole binary system

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Let's assume that you had a black hole binary system and everything said here is possible. Their large masses would lead to a large emission of gravitational waves. The loss of orbital energy and angular momentum to this gravitational radiation should ultimately cause the two black holes to merge into a single black hole containing the combined mass of the merged black holes.

With this said, does a greater combined mass of the newly formed black hole mean that the radius of the new event horizon is greater than the radius of the event horizons of the singular black holes? I don't know if there is a formula connecting mass to radius, or if this is essentially a conceptually hypothetical concept, and the answer is simply that the larger the mass of the black hole, the larger the radius of its event horizon

The "radius" (there is no physical surface) of the event horizon of a rotating black hole, depends on both it's mass $M$ and angular momentum $J$, and is given by the equation $$r = frac{GM}{c^2} +sqrt{left(frac{GM}{c^2} ight)^2- left(frac{J}{Mc} ight)^2}.$$

It is thus difficult (for me anyway) to give a straightforward answer to your question. When two black holes merge, they will each have their own masses and angular momenta, plus there will be angular momentum in the orbit. The gravitational waves emitted during the merger can take away mass from the system as a whole (e.g. the final mass of the first observed black hole merger was three solar masses less than the summed masses of the merging components).

So, in general yes, for non-spinning black holes the event horizon grows as the total mass. But if the merger results in a black hole with maximal spin, where $J = GM^2/c$, then the final event horizon could be half the size given by the Schwarzschild radius ($2GM/c^2$), even though the total mass is larger than the black holes that contributed to it.

However, I think what is certainly true, is that it is not possible to add mass (even in the form of another black hole) to a given black hole and for the event horizon to get smaller, whatever the angular momentum contributed by that mass (section 4.2 of "Black Holes", by Raine & Thomas, 2015, Imperial College Press).

Yes, there is a simple formula connecting mass with radius. It is called the Schwarzschild radius. It is really well explained in Wikipedia, with examples.

Quoting:

The Schwarzschild radius is the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface of the sphere would equal the speed of light.

Formula: $$r_s = frac{2MG}{c^2}$$ As you can see, with exception of radius and mass itself, all other are constants (c = speed of light, G = gravitational constant). So the double the mass, the double the radius.

Therefore yes, after merging the size would be greater (I think this is your original question), althought not sure if it is the exact sum due to some kind of energy loss during the merge. As a side note, there is no need of having a binary system of black holes colliding in order to determine or change the size of a black hole, it can grow just by eating surrounding particles, gas, etc.

## Approximating a black hole merger with a Schwarzschild-based model?

Summary: Can a black hole merger be approximated as a daughter Schwarzschild black hole created when two parent Schwarzschild black holes pack close enough together to trigger a local Schwarzschild radius containing their combined mass?

We know that the radius of the event horizon of a Schwarzschild black hole (SBH) is defined as r_s = 2*G*M/c^2, corresponding to the radius at which the escape velocity is the speed of light. For a binary black hole system, M_1 is the mass of the larger black hole and M_2 is the mass of the smaller. The LIGO event was of the merger of a 36 M_sun (where M_sun is the mass of the sun) black hole and a 29 M_sun black hole, radiating 3 M_sun equivalent energy before resulting in a 62 M_sun black hole. Thus, the larger SBH would have a Schwarzschild radius (SR) of 106 km and the smaller one would have an SR of 86 km.

If we model this super simplistically, then could we say that the black holes "merged" when they approached close enough to trigger an SBH in their vicinity? I attempted to illustrate this in the figure below.

Here, r_s1 is the radius of the larger SBH, r_s2 is the radius of the smaller SBH, x_c1 is the distance from the larger SBH to the system's barycenter, and x_c2 is the distance from the smaller SBH to the system's barycenter. For a sphere centered at the barycenter with the combined system mass of 65 M_sun (the sum of the masses of the two merging SBH's), the two black holes would enter the sphere starting at x_c2 = r_s3, where r_s3 is the SR of the equivalent SBH that would exist as a replacement of the two parent black holes. Here, x_c2 = r_s3 = 192 km. Using the equation for the position of the center of mass of two point masses, we get that x_c1 = M_2/M_1*r_s3, where M_1 is the mass of the larger SBH and M_2 is the mass of the smaller SBH. Thus, the distance between the two black holes at the time of the "merge" would be d_merge = (1+M_2/M_1)*r_s3, where d_merge is the distance between them at that moment. Could we then state that the black holes "merged" when their centers were 347 km apart? We could then model the gravitational energy emission at the moment of the merger as an instantaneous decay of the merged SBH with an SR of 192 km to a "stable" SBH with an SR of 183 km. It is of course simple to note that r_s3 = r_s1+r_s2, and that d_merge > (r_s1+r_s2), meaning that the event horizons of the two merging SBH's do not touch before the merge and are in fact separated by d_separation = d_merge-r_s1-r_s2 = d_merge-r_s3 = 155 km, where d_separation is the minimum distance between the two parent event horizons.

I know that I am neglected the fact that the space occupied by the two black holes is not uniformly dense.

Do merging black holes lose information? They absolutely must, according to General Relativity and the known laws of physics. Take two black holes, merge them together, and they lose mass. For the ten black hole-black hole mergers LIGO and Virgo have seen so far, each one has lost mass in the process: about 5% of the total, on average. So where does the information that was encoded by that mass go? That’s what our Patreon supporter Pierre Fransson wants to know, asking:

When black holes merge they [lose] energy through gravitational waves. Does this pose the same problem as Hawking radiation does, with respect to loss of information? Or is the information on what has gone into the black hole somehow encoded into the gravitational wave? And if it is could we someday hope to decode what went into the black hole using gravitational waves?

Let’s take a look at black hole information in general, and then let’s examine what happens when they merge.

Black holes used to present a tremendous puzzle for astrophysicists when it came to the idea of information. No matter what it is that you make your black hole out of — whether it’s stars, atoms, protons, electrons, antimatter, heavy elements, or exotic particles — there are only three things that matter for the properties a black hole possesses: its total mass, electric charge, and angular momentum.

Whether you made a black hole out of ten solar masses of oxygen atoms, uranium atoms, or antiprotons-and-positrons should be completely irrelevant to what you find. Quantities like baryon number, lepton number, isospin, and a slew of other particle properties don’t play any role in the physics of a black hole. Once you fall inside, that information should be lost forever.

At least, that’s what happens in General Relativity all by itself.

The story changes, however, if you start to consider things like thermodynamics and quantum physics. Without those considerations, General Relativity tells you what a black hole’s entropy is: zero.

That should set off alarm bells in your head. Obviously, that cannot be right. Everything that has a temperature, energy, and particle properties has a non-zero entropy, and entropy can never decrease. If the matter that you made black holes out of had a non-zero entropy, then by throwing that material into a black hole, entropy would have to go up or stay the same it could never go down. A black hole must have a finite, positive, and non-zero entropy to account for all the matter that falls into it.

While we conventionally think of entropy as something like “information content” or “disorder,” neither one of those definitions truly encapsulates what it physically is. Instead, it’s better to think of entropy as the number of possible configurations that a quantum state could theoretically possess.

Whenever a quantum particle falls into a black hole’s event horizon, it has a number of particle properties inherent to it, including spin, charge, mass, polarization, baryon number, lepton number, and many others. If the singularity at a black hole’s center doesn’t depend on those properties, there must be some other location that stores that information. John Wheeler was the first person to realize where it could be stored: the event horizon. By considering what an outside observer would see as a quantum particle (or a set of particles) fell into a black hole’s event horizon, we can understand how entropy — or information, if you like — gets encoded.

From far away, something falling in would appear to asymptotically approach the event horizon, spaghettifying in the process. Its apparent color would turn redder and redder due to the effects of gravitational redshift, and the amount of time to cross the horizon would asymptote to infinity, as relativistic time dilation took effect. The information from anything that falls into a black hole must appear to be encoded along the surface of the event horizon.

Since a black hole’s mass determines the size of its event horizon, this gave a natural place for the entropy of a black hole to exist: on the surface area of the event horizon. As a black hole grows, its event horizon grows, accommodating the additional entropy and information of whatever falls in.

Instead of zero, the entropy of black holes would be enormous, based on the number of quantum bits that could be encoded on an event horizon of a particular size.

10^-66 m²), where the entire amount of information that can be encoded is proportional to the event horizon’s surface area. (T.B. BAKKER / DR. J.P. VAN DER SCHAAR, UNIVERSITEIT VAN AMSTERDAM)

And that brings us to the problem of merging black holes. We now have two of them, in orbit around one another, with a tremendous amount of entropy encoded on their surfaces. Let’s imagine we have two black holes of roughly equal masses, which more-or-less corresponds to the black hole mergers LIGO and Virgo have seen. Black hole #1 has a certain mass (M) and a amount of entropy: let’s call it S. Black hole #2, if it’s the same mass (M) as #1, also has S for its entropy.

Now, let’s imagine them merged together. In the end, the new black hole will have almost (but not quite) double the original mass its new mass will be the sum of both black hole #1 and black hole #2, minus about 5%. All told, its total mass will be 1.9M, assuming each black hole lost 5% of its mass. This means there’s a set of gravitational waves traveling through the Universe carrying that missing energy: 0.1Mc2, where mass is converted into energy by Einstein’s famous rule.

But here’s where we run into the big conundrum that demonstrates how difficult it is to answer the question of where the entropy (or information) goes when black holes merge. You can imagine three possible solutions:

1. The information from both black holes remains entirely encoded on the event horizon of the new, larger-mass black hole. The gravitational waves carry none.
2. The maximal amount of information possible gets encoded onto the gravitational waves: these energy-carrying waves are also entropy-carrying waves, leaving the merger remnant with the least amount of entropy possible.
3. The information gets split in some non-maximal way between the new event horizon and the gravitational waves themselves.

Unfortunately for all of us, all three possibilities are allowed.

361% the surface area of either progenitor. (LIGO/VIRGO/NORTHWESTERN UNIV./FRANK ELAVSKY)

Remember what we said about the amount of entropy that a black hole can possess: it’s proportional to the event horizon’s surface area. But that surface area is proportional to the mass squared, which means that if black hole #1 had an entropy of S and black hole #2 had an entropy of S, then a black hole with 1.9 times the mass of #1 and #2 would have an entropy of

3.6S, enough to easily hold the information of both progenitor black holes. This is the Bekenstein-Hawking entropy.

On the other hand, gravitational waves can carry entropy, too, just like any wave can. And it’s not like we can just calculate how much quantum information is in those waves like we can for photons without an understanding of the underlying quantum (gravitational) processes at play, we are limited in how much we can say about the entropy carried by gravitational waves from merging black holes.

But we can say something of great importance here: the gravitational waves must carry some entropy themselves. During the inspiral phase preceding the merger, these two event horizons are practically unchanged, yet the system is losing mass and energy as the two massive black holes approach one another in space. The gravitational waves carry that energy away, and must also carry the information-and-entropy associated with that energy change with them.

Throughout the entirety of the merger, these gravitational waves are being generated by the changes in curved space itself, and the energy for those waves comes from the changing configuration of the matter-and-energy distribution of the fabric of space. But how much of the information from either of the two event horizons makes it out and into the waves, though, is a question we cannot answer at present, either theoretically or observationally.

Information doesn’t get lost when two black holes merge, since the final state is known to have a greater entropy than either initial state, so it’s not the same as the problem of Hawking radiation. But we cannot say with any certainty how the entropy encoded on those two black hole event horizons gets transferred into the new event horizon and outgoing gravitational wave system we wind up with in the end.

Observationally, we have no way of extracting any sort of entropic or informational signal from gravitational waves at present. Nor can we measure the entropy encoded on an event horizon. We have every reason to believe that information is preserved, and that most of the information from the progenitor black holes winds up in the merged product. But until we find a way to measure and quantify the entropy in black holes and gravitational waves, we must confess to our own ignorance.

## Contents

The idea of a body so massive that even light could not escape was briefly proposed by astronomical pioneer and English clergyman John Michell in a letter published in November 1784. Michell's simplistic calculations assumed such a body might have the same density as the Sun, and concluded that such a body would form when a star's diameter exceeds the Sun's by a factor of 500, and the surface escape velocity exceeds the usual speed of light. Michell correctly noted that such supermassive but non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies. [7] [25] [26] Scholars of the time were initially excited by the proposal that giant but invisible stars might be hiding in plain view, but enthusiasm dampened when the wavelike nature of light became apparent in the early nineteenth century. [27]

If light were a wave rather than a "corpuscle", it is unclear what, if any, influence gravity would have on escaping light waves. [7] [26] Modern physics discredits Michell's notion of a light ray shooting directly from the surface of a supermassive star, being slowed down by the star's gravity, stopping, and then free-falling back to the star's surface. [28]

### General relativity

In 1915, Albert Einstein developed his theory of general relativity, having earlier shown that gravity does influence light's motion. Only a few months later, Karl Schwarzschild found a solution to the Einstein field equations, which describes the gravitational field of a point mass and a spherical mass. [29] A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass and wrote more extensively about its properties. [30] [31] This solution had a peculiar behaviour at what is now called the Schwarzschild radius, where it became singular, meaning that some of the terms in the Einstein equations became infinite. The nature of this surface was not quite understood at the time. In 1924, Arthur Eddington showed that the singularity disappeared after a change of coordinates (see Eddington–Finkelstein coordinates), although it took until 1933 for Georges Lemaître to realize that this meant the singularity at the Schwarzschild radius was a non-physical coordinate singularity. [32] Arthur Eddington did however comment on the possibility of a star with mass compressed to the Schwarzschild radius in a 1926 book, noting that Einstein's theory allows us to rule out overly large densities for visible stars like Betelgeuse because "a star of 250 million km radius could not possibly have so high a density as the Sun. Firstly, the force of gravitation would be so great that light would be unable to escape from it, the rays falling back to the star like a stone to the earth. Secondly, the red shift of the spectral lines would be so great that the spectrum would be shifted out of existence. Thirdly, the mass would produce so much curvature of the spacetime metric that space would close up around the star, leaving us outside (i.e., nowhere)." [33] [34]

In 1931, Subrahmanyan Chandrasekhar calculated, using special relativity, that a non-rotating body of electron-degenerate matter above a certain limiting mass (now called the Chandrasekhar limit at 1.4 M ) has no stable solutions. [35] His arguments were opposed by many of his contemporaries like Eddington and Lev Landau, who argued that some yet unknown mechanism would stop the collapse. [36] They were partly correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star, [37] which is itself stable. But in 1939, Robert Oppenheimer and others predicted that neutron stars above another limit (the Tolman–Oppenheimer–Volkoff limit) would collapse further for the reasons presented by Chandrasekhar, and concluded that no law of physics was likely to intervene and stop at least some stars from collapsing to black holes. [38] Their original calculations, based on the Pauli exclusion principle, gave it as 0.7 M subsequent consideration of strong force-mediated neutron-neutron repulsion raised the estimate to approximately 1.5 M to 3.0 M . [39] Observations of the neutron star merger GW170817, which is thought to have generated a black hole shortly afterward, have refined the TOV limit estimate to

Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infalling observers. Because of this property, the collapsed stars were called "frozen stars", because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it to the Schwarzschild radius. [45]

#### Golden age

In 1958, David Finkelstein identified the Schwarzschild surface as an event horizon, "a perfect unidirectional membrane: causal influences can cross it in only one direction". [46] This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. Finkelstein's solution extended the Schwarzschild solution for the future of observers falling into a black hole. A complete extension had already been found by Martin Kruskal, who was urged to publish it. [47]

These results came at the beginning of the golden age of general relativity, which was marked by general relativity and black holes becoming mainstream subjects of research. This process was helped by the discovery of pulsars by Jocelyn Bell Burnell in 1967, [48] [49] which, by 1969, were shown to be rapidly rotating neutron stars. [50] Until that time, neutron stars, like black holes, were regarded as just theoretical curiosities but the discovery of pulsars showed their physical relevance and spurred a further interest in all types of compact objects that might be formed by gravitational collapse. [ citation needed ]

In this period more general black hole solutions were found. In 1963, Roy Kerr found the exact solution for a rotating black hole. Two years later, Ezra Newman found the axisymmetric solution for a black hole that is both rotating and electrically charged. [51] Through the work of Werner Israel, [52] Brandon Carter, [53] [54] and David Robinson [55] the no-hair theorem emerged, stating that a stationary black hole solution is completely described by the three parameters of the Kerr–Newman metric: mass, angular momentum, and electric charge. [56]

At first, it was suspected that the strange features of the black hole solutions were pathological artifacts from the symmetry conditions imposed, and that the singularities would not appear in generic situations. This view was held in particular by Vladimir Belinsky, Isaak Khalatnikov, and Evgeny Lifshitz, who tried to prove that no singularities appear in generic solutions. However, in the late 1960s Roger Penrose [57] and Stephen Hawking used global techniques to prove that singularities appear generically. [58] For this work, Penrose received half of the 2020 Nobel Prize in Physics, Hawking having died in 2018. [59] Based on observations in Greenwich and Toronto in the early 1970s, Cygnus X-1, a galactic X-ray source discovered in 1964, became the first astronomical object commonly accepted to be a black hole. [60] [61]

Work by James Bardeen, Jacob Bekenstein, Carter, and Hawking in the early 1970s led to the formulation of black hole thermodynamics. [62] These laws describe the behaviour of a black hole in close analogy to the laws of thermodynamics by relating mass to energy, area to entropy, and surface gravity to temperature. The analogy was completed when Hawking, in 1974, showed that quantum field theory implies that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole, predicting the effect now known as Hawking radiation. [63]

### Etymology

John Michell used the term "dark star", [64] and in the early 20th century, physicists used the term "gravitationally collapsed object". Science writer Marcia Bartusiak traces the term "black hole" to physicist Robert H. Dicke, who in the early 1960s reportedly compared the phenomenon to the Black Hole of Calcutta, notorious as a prison where people entered but never left alive. [65]

The term "black hole" was used in print by Life and Science News magazines in 1963, [65] and by science journalist Ann Ewing in her article " 'Black Holes' in Space", dated 18 January 1964, which was a report on a meeting of the American Association for the Advancement of Science held in Cleveland, Ohio. [66] [67]

In December 1967, a student reportedly suggested the phrase "black hole" at a lecture by John Wheeler [66] Wheeler adopted the term for its brevity and "advertising value", and it quickly caught on, [68] leading some to credit Wheeler with coining the phrase. [69]

The no-hair theorem postulates that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, electric charge, and angular momentum the black hole is otherwise featureless. If the conjecture is true, any two black holes that share the same values for these properties, or parameters, are indistinguishable from one another. The degree to which the conjecture is true for real black holes under the laws of modern physics is currently an unsolved problem. [56]

These properties are special because they are visible from outside a black hole. For example, a charged black hole repels other like charges just like any other charged object. Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law (through the ADM mass), far away from the black hole. [70] Likewise, the angular momentum (or spin) can be measured from far away using frame dragging by the gravitomagnetic field, through for example the Lense–Thirring effect. [71]

When an object falls into a black hole, any information about the shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers. The behavior of the horizon in this situation is a dissipative system that is closely analogous to that of a conductive stretchy membrane with friction and electrical resistance—the membrane paradigm. [72] This is different from other field theories such as electromagnetism, which do not have any friction or resistivity at the microscopic level, because they are time-reversible. Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in. The information that is lost includes every quantity that cannot be measured far away from the black hole horizon, including approximately conserved quantum numbers such as the total baryon number and lepton number. This behavior is so puzzling that it has been called the black hole information loss paradox. [73] [74]

### Physical properties

The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916. [29] According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric. [75] This means there is no observable difference at a distance between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore correct only near a black hole's horizon far away, the external gravitational field is identical to that of any other body of the same mass. [76]

Solutions describing more general black holes also exist. Non-rotating charged black holes are described by the Reissner–Nordström metric, while the Kerr metric describes a non-charged rotating black hole. The most general stationary black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum. [77]

While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. The total electric charge Q and the total angular momentum J are expected to satisfy

for a black hole of mass M. Black holes with the minimum possible mass satisfying this inequality are called extremal. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have so-called naked singularities that can be observed from the outside, and hence are deemed unphysical. The cosmic censorship hypothesis rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter. [2] This is supported by numerical simulations. [78]

Due to the relatively large strength of the electromagnetic force, black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a universal feature of compact astrophysical objects. The black-hole candidate binary X-ray source GRS 1915+105 [79] appears to have an angular momentum near the maximum allowed value. That uncharged limit is [80]

allowing definition of a dimensionless spin parameter such that [80]

0 ≤ c J G M 2 ≤ 1. >>leq 1.> [80] [Note 1]

Black hole classifications
Class Approx.
mass
Approx.
Supermassive black hole 10 5 –10 10 M 0.001–400 AU
Intermediate-mass black hole 10 3 M 10 3 km ≈ REarth
Stellar black hole 10 M 30 km
Micro black hole up to MMoon up to 0.1 mm

Black holes are commonly classified according to their mass, independent of angular momentum, J. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is proportional to the mass, M, through

where rs is the Schwarzschild radius and M is the mass of the Sun. [82] For a black hole with nonzero spin and/or electric charge, the radius is smaller, [Note 2] until an extremal black hole could have an event horizon close to [83]

### Event horizon

The defining feature of a black hole is the appearance of an event horizon—a boundary in spacetime through which matter and light can pass only inward towards the mass of the black hole. Nothing, not even light, can escape from inside the event horizon. [85] [86] The event horizon is referred to as such because if an event occurs within the boundary, information from that event cannot reach an outside observer, making it impossible to determine whether such an event occurred. [87]

As predicted by general relativity, the presence of a mass deforms spacetime in such a way that the paths taken by particles bend towards the mass. [88] At the event horizon of a black hole, this deformation becomes so strong that there are no paths that lead away from the black hole. [89]

To a distant observer, clocks near a black hole would appear to tick more slowly than those further away from the black hole. [90] Due to this effect, known as gravitational time dilation, an object falling into a black hole appears to slow as it approaches the event horizon, taking an infinite time to reach it. [91] At the same time, all processes on this object slow down, from the viewpoint of a fixed outside observer, causing any light emitted by the object to appear redder and dimmer, an effect known as gravitational redshift. [92] Eventually, the falling object fades away until it can no longer be seen. Typically this process happens very rapidly with an object disappearing from view within less than a second. [93]

On the other hand, indestructible observers falling into a black hole do not notice any of these effects as they cross the event horizon. According to their own clocks, which appear to them to tick normally, they cross the event horizon after a finite time without noting any singular behaviour in classical general relativity, it is impossible to determine the location of the event horizon from local observations, due to Einstein's equivalence principle. [94] [95]

The topology of the event horizon of a black hole at equilibrium is always spherical. [Note 4] [98] For non-rotating (static) black holes the geometry of the event horizon is precisely spherical, while for rotating black holes the event horizon is oblate. [99] [100] [101]

### Singularity

At the center of a black hole, as described by general relativity, may lie a gravitational singularity, a region where the spacetime curvature becomes infinite. [102] For a non-rotating black hole, this region takes the shape of a single point and for a rotating black hole, it is smeared out to form a ring singularity that lies in the plane of rotation. [103] In both cases, the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution. [104] The singular region can thus be thought of as having infinite density. [105]

Observers falling into a Schwarzschild black hole (i.e., non-rotating and not charged) cannot avoid being carried into the singularity once they cross the event horizon. They can prolong the experience by accelerating away to slow their descent, but only up to a limit. [106] When they reach the singularity, they are crushed to infinite density and their mass is added to the total of the black hole. Before that happens, they will have been torn apart by the growing tidal forces in a process sometimes referred to as spaghettification or the "noodle effect". [107]

In the case of a charged (Reissner–Nordström) or rotating (Kerr) black hole, it is possible to avoid the singularity. Extending these solutions as far as possible reveals the hypothetical possibility of exiting the black hole into a different spacetime with the black hole acting as a wormhole. [108] The possibility of traveling to another universe is, however, only theoretical since any perturbation would destroy this possibility. [109] It also appears to be possible to follow closed timelike curves (returning to one's own past) around the Kerr singularity, which leads to problems with causality like the grandfather paradox. [110] It is expected that none of these peculiar effects would survive in a proper quantum treatment of rotating and charged black holes. [111]

The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. [112] This breakdown, however, is expected it occurs in a situation where quantum effects should describe these actions, due to the extremely high density and therefore particle interactions. To date, it has not been possible to combine quantum and gravitational effects into a single theory, although there exist attempts to formulate such a theory of quantum gravity. It is generally expected that such a theory will not feature any singularities. [113] [114]

### Photon sphere

The photon sphere is a spherical boundary of zero thickness in which photons that move on tangents to that sphere would be trapped in a circular orbit about the black hole. For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. Their orbits would be dynamically unstable, hence any small perturbation, such as a particle of infalling matter, would cause an instability that would grow over time, either setting the photon on an outward trajectory causing it to escape the black hole, or on an inward spiral where it would eventually cross the event horizon. [115]

While light can still escape from the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light that reaches an outside observer from the photon sphere must have been emitted by objects between the photon sphere and the event horizon. [115] For a Kerr black hole the radius of the photon sphere depends on the spin parameter and on the details of the photon orbit, which can be prograde (the photon rotates in the same sense of the black hole spin) or retrograde. [116] [117]

### Ergosphere

Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This is the result of a process known as frame-dragging general relativity predicts that any rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it. Any object near the rotating mass will tend to start moving in the direction of rotation. For a rotating black hole, this effect is so strong near the event horizon that an object would have to move faster than the speed of light in the opposite direction to just stand still. [119]

The ergosphere of a black hole is a volume bounded by the black hole's event horizon and the ergosurface, which coincides with the event horizon at the poles but is at a much greater distance around the equator. [118]

Objects and radiation can escape normally from the ergosphere. Through the Penrose process, objects can emerge from the ergosphere with more energy than they entered with. The extra energy is taken from the rotational energy of the black hole. Thereby the rotation of the black hole slows down. [120] A variation of the Penrose process in the presence of strong magnetic fields, the Blandford–Znajek process is considered a likely mechanism for the enormous luminosity and relativistic jets of quasars and other active galactic nuclei.

### Innermost stable circular orbit (ISCO)

In Newtonian gravity, test particles can stably orbit at arbitrary distances from a central object. In general relativity, however, there exists an innermost stable circular orbit (often called the ISCO), inside of which, any infinitesimal perturbations to a circular orbit will lead to inspiral into the black hole. [121] The location of the ISCO depends on the spin of the black hole, in the case of a Schwarzschild black hole (spin zero) is:

and decreases with increasing black hole spin for particles orbiting in the same direction as the spin. [122]

Given the bizarre character of black holes, it was long questioned whether such objects could actually exist in nature or whether they were merely pathological solutions to Einstein's equations. Einstein himself wrongly thought black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius. [123] This led the general relativity community to dismiss all results to the contrary for many years. However, a minority of relativists continued to contend that black holes were physical objects, [124] and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to the formation of an event horizon. [ citation needed ]

Penrose demonstrated that once an event horizon forms, general relativity without quantum mechanics requires that a singularity will form within. [57] Shortly afterwards, Hawking showed that many cosmological solutions that describe the Big Bang have singularities without scalar fields or other exotic matter (see "Penrose–Hawking singularity theorems"). [ clarification needed ] The Kerr solution, the no-hair theorem, and the laws of black hole thermodynamics showed that the physical properties of black holes were simple and comprehensible, making them respectable subjects for research. [125] Conventional black holes are formed by gravitational collapse of heavy objects such as stars, but they can also in theory be formed by other processes. [126] [127]

### Gravitational collapse

Gravitational collapse occurs when an object's internal pressure is insufficient to resist the object's own gravity. For stars this usually occurs either because a star has too little "fuel" left to maintain its temperature through stellar nucleosynthesis, or because a star that would have been stable receives extra matter in a way that does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight. [128] The collapse may be stopped by the degeneracy pressure of the star's constituents, allowing the condensation of matter into an exotic denser state. The result is one of the various types of compact star. Which type forms depends on the mass of the remnant of the original star left if the outer layers have been blown away (for example, in a Type II supernova). The mass of the remnant, the collapsed object that survives the explosion, can be substantially less than that of the original star. Remnants exceeding 5 M are produced by stars that were over 20 M before the collapse. [128]

If the mass of the remnant exceeds about 3–4 M (the Tolman–Oppenheimer–Volkoff limit [38] ), either because the original star was very heavy or because the remnant collected additional mass through accretion of matter, even the degeneracy pressure of neutrons is insufficient to stop the collapse. No known mechanism (except possibly quark degeneracy pressure, see quark star) is powerful enough to stop the implosion and the object will inevitably collapse to form a black hole. [128]

The gravitational collapse of heavy stars is assumed to be responsible for the formation of stellar mass black holes. Star formation in the early universe may have resulted in very massive stars, which upon their collapse would have produced black holes of up to 10 3 M . These black holes could be the seeds of the supermassive black holes found in the centers of most galaxies. [130] It has further been suggested that massive black holes with typical masses of

10 5 M could have formed from the direct collapse of gas clouds in the young universe. [126] These massive objects have been proposed as the seeds that eventually formed the earliest quasars observed already at redshift z ∼ 7 . [131] Some candidates for such objects have been found in observations of the young universe. [126]

While most of the energy released during gravitational collapse is emitted very quickly, an outside observer does not actually see the end of this process. Even though the collapse takes a finite amount of time from the reference frame of infalling matter, a distant observer would see the infalling material slow and halt just above the event horizon, due to gravitational time dilation. Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms delayed an infinite amount of time. Thus the external observer never sees the formation of the event horizon instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away. [132]

#### Primordial black holes and the Big Bang

Gravitational collapse requires great density. In the current epoch of the universe these high densities are found only in stars, but in the early universe shortly after the Big Bang densities were much greater, possibly allowing for the creation of black holes. High density alone is not enough to allow black hole formation since a uniform mass distribution will not allow the mass to bunch up. In order for primordial black holes to have formed in such a dense medium, there must have been initial density perturbations that could then grow under their own gravity. Different models for the early universe vary widely in their predictions of the scale of these fluctuations. Various models predict the creation of primordial black holes ranging in size from a Planck mass (mP= √ ħc/G ≈ 1.2 × 10 19 GeV/c 2 ≈ 2.2 × 10 −8 kg ) to hundreds of thousands of solar masses. [127]

Despite the early universe being extremely dense—far denser than is usually required to form a black hole—it did not re-collapse into a black hole during the Big Bang. Models for the gravitational collapse of objects of relatively constant size, such as stars, do not necessarily apply in the same way to rapidly expanding space such as the Big Bang. [133]

### High-energy collisions

Gravitational collapse is not the only process that could create black holes. In principle, black holes could be formed in high-energy collisions that achieve sufficient density. As of 2002, no such events have been detected, either directly or indirectly as a deficiency of the mass balance in particle accelerator experiments. [134] This suggests that there must be a lower limit for the mass of black holes. Theoretically, this boundary is expected to lie around the Planck mass, where quantum effects are expected to invalidate the predictions of general relativity. [135] This would put the creation of black holes firmly out of reach of any high-energy process occurring on or near the Earth. However, certain developments in quantum gravity suggest that the minimum black hole mass could be much lower: some braneworld scenarios for example put the boundary as low as 1 TeV/c 2 . [136] This would make it conceivable for micro black holes to be created in the high-energy collisions that occur when cosmic rays hit the Earth's atmosphere, or possibly in the Large Hadron Collider at CERN. These theories are very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists. [137] Even if micro black holes could be formed, it is expected that they would evaporate in about 10 −25 seconds, posing no threat to the Earth. [138]

### Growth

Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas and interstellar dust from its surroundings. This growth process is one possible way through which some supermassive black holes may have been formed, although the formation of supermassive black holes is still an open field of research. [130] A similar process has been suggested for the formation of intermediate-mass black holes found in globular clusters. [139] Black holes can also merge with other objects such as stars or even other black holes. This is thought to have been important, especially in the early growth of supermassive black holes, which could have formed from the aggregation of many smaller objects. [130] The process has also been proposed as the origin of some intermediate-mass black holes. [140] [141]

### Evaporation

In 1974, Hawking predicted that black holes are not entirely black but emit small amounts of thermal radiation at a temperature ℏc 3 /(8πGMkB) [63] this effect has become known as Hawking radiation. By applying quantum field theory to a static black hole background, he determined that a black hole should emit particles that display a perfect black body spectrum. Since Hawking's publication, many others have verified the result through various approaches. [142] If Hawking's theory of black hole radiation is correct, then black holes are expected to shrink and evaporate over time as they lose mass by the emission of photons and other particles. [63] The temperature of this thermal spectrum (Hawking temperature) is proportional to the surface gravity of the black hole, which, for a Schwarzschild black hole, is inversely proportional to the mass. Hence, large black holes emit less radiation than small black holes. [143]

A stellar black hole of 1 M has a Hawking temperature of 62 nanokelvins. [144] This is far less than the 2.7 K temperature of the cosmic microwave background radiation. Stellar-mass or larger black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and thus will grow instead of shrinking. [145] To have a Hawking temperature larger than 2.7 K (and be able to evaporate), a black hole would need a mass less than the Moon. Such a black hole would have a diameter of less than a tenth of a millimeter. [146]

If a black hole is very small, the radiation effects are expected to become very strong. A black hole with the mass of a car would have a diameter of about 10 −24 m and take a nanosecond to evaporate, during which time it would briefly have a luminosity of more than 200 times that of the Sun. Lower-mass black holes are expected to evaporate even faster for example, a black hole of mass 1 TeV/c 2 would take less than 10 −88 seconds to evaporate completely. For such a small black hole, quantum gravity effects are expected to play an important role and could hypothetically make such a small black hole stable, although current developments in quantum gravity do not indicate this is the case. [147] [148]

The Hawking radiation for an astrophysical black hole is predicted to be very weak and would thus be exceedingly difficult to detect from Earth. A possible exception, however, is the burst of gamma rays emitted in the last stage of the evaporation of primordial black holes. Searches for such flashes have proven unsuccessful and provide stringent limits on the possibility of existence of low mass primordial black holes. [149] NASA's Fermi Gamma-ray Space Telescope launched in 2008 will continue the search for these flashes. [150]

If black holes evaporate via Hawking radiation, a solar mass black hole will evaporate (beginning once the temperature of the cosmic microwave background drops below that of the black hole) over a period of 10 64 years. [151] A supermassive black hole with a mass of 10 11 M will evaporate in around 2×10 100 years. [152] Some monster black holes in the universe are predicted to continue to grow up to perhaps 10 14 M during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 10 106 years. [151]

By nature, black holes do not themselves emit any electromagnetic radiation other than the hypothetical Hawking radiation, so astrophysicists searching for black holes must generally rely on indirect observations. For example, a black hole's existence can sometimes be inferred by observing its gravitational influence upon its surroundings. [153]

On 10 April 2019 an image was released of a black hole, which is seen in magnified fashion because the light paths near the event horizon are highly bent. The dark shadow in the middle results from light paths absorbed by the black hole. [22] The image is in false color, as the detected light halo in this image is not in the visible spectrum, but radio waves.

The Event Horizon Telescope (EHT), is an active program that directly observes the immediate environment of the event horizon of black holes, such as the black hole at the centre of the Milky Way. In April 2017, EHT began observation of the black hole in the center of Messier 87. [154] "In all, eight radio observatories on six mountains and four continents observed the galaxy in Virgo on and off for 10 days in April 2017" to provide the data yielding the image two years later in April 2019. [155] After two years of data processing, EHT released the first direct image of a black hole, specifically the supermassive black hole that lies in the center of the aforementioned galaxy. [156] [157] What is visible is not the black hole, which shows as black because of the loss of all light within this dark region, rather it is the gases at the edge of the event horizon, which are displayed as orange or red, that define the black hole. [158]

The brightening of this material in the 'bottom' half of the processed EHT image is thought to be caused by Doppler beaming, whereby material approaching the viewer at relativistic speeds is perceived as brighter than material moving away. In the case of a black hole, this phenomenon implies that the visible material is rotating at relativistic speeds (>1,000 km/s), the only speeds at which it is possible to centrifugally balance the immense gravitational attraction of the singularity, and thereby remain in orbit above the event horizon. This configuration of bright material implies that the EHT observed M87* from a perspective catching the black hole's accretion disc nearly edge-on, as the whole system rotated clockwise. [159] [160] However, the extreme gravitational lensing associated with black holes produces the illusion of a perspective that sees the accretion disc from above. In reality, most of the ring in the EHT image was created when the light emitted by the far side of the accretion disc bent around the black hole's gravity well and escaped this means that most of the possible perspectives on M87* can see the entire disc, even that directly behind the "shadow".

Prior to this, in 2015, the EHT detected magnetic fields just outside the event horizon of Sagittarius A*, and even discerned some of their properties. The field lines that pass through the accretion disc were found to be a complex mixture of ordered and tangled. The existence of magnetic fields had been predicted by theoretical studies of black holes. [161] [162]

### Detection of gravitational waves from merging black holes

On 14 September 2015 the LIGO gravitational wave observatory made the first-ever successful direct observation of gravitational waves. [11] [164] The signal was consistent with theoretical predictions for the gravitational waves produced by the merger of two black holes: one with about 36 solar masses, and the other around 29 solar masses. [11] [165] This observation provides the most concrete evidence for the existence of black holes to date. For instance, the gravitational wave signal suggests that the separation of the two objects prior to the merger was just 350 km (or roughly four times the Schwarzschild radius corresponding to the inferred masses). The objects must therefore have been extremely compact, leaving black holes as the most plausible interpretation. [11]

More importantly, the signal observed by LIGO also included the start of the post-merger ringdown, the signal produced as the newly formed compact object settles down to a stationary state. Arguably, the ringdown is the most direct way of observing a black hole. [166] From the LIGO signal it is possible to extract the frequency and damping time of the dominant mode of the ringdown. From these it is possible to infer the mass and angular momentum of the final object, which match independent predictions from numerical simulations of the merger. [167] The frequency and decay time of the dominant mode are determined by the geometry of the photon sphere. Hence, observation of this mode confirms the presence of a photon sphere however, it cannot exclude possible exotic alternatives to black holes that are compact enough to have a photon sphere. [166]

The observation also provides the first observational evidence for the existence of stellar-mass black hole binaries. Furthermore, it is the first observational evidence of stellar-mass black holes weighing 25 solar masses or more. [168]

Since then many more gravitational wave events have been observed. [13]

### Proper motions of stars orbiting Sagittarius A*

The proper motions of stars near the center of our own Milky Way provide strong observational evidence that these stars are orbiting a supermassive black hole. [169] Since 1995, astronomers have tracked the motions of 90 stars orbiting an invisible object coincident with the radio source Sagittarius A*. By fitting their motions to Keplerian orbits, the astronomers were able to infer, in 1998, that a 2.6 × 10 6 M object must be contained in a volume with a radius of 0.02 light-years to cause the motions of those stars. [170] Since then, one of the stars—called S2—has completed a full orbit. From the orbital data, astronomers were able to refine the calculations of the mass to 4.3 × 10 6 M and a radius of less than 0.002 light-years for the object causing the orbital motion of those stars. [169] The upper limit on the object's size is still too large to test whether it is smaller than its Schwarzschild radius nevertheless, these observations strongly suggest that the central object is a supermassive black hole as there are no other plausible scenarios for confining so much invisible mass into such a small volume. [170] Additionally, there is some observational evidence that this object might possess an event horizon, a feature unique to black holes. [171]

### Accretion of matter

Due to conservation of angular momentum, [173] gas falling into the gravitational well created by a massive object will typically form a disk-like structure around the object. Artists' impressions such as the accompanying representation of a black hole with corona commonly depict the black hole as if it were a flat-space body hiding the part of the disk just behind it, but in reality gravitational lensing would greatly distort the image of the accretion disk. [174]

Within such a disk, friction would cause angular momentum to be transported outward, allowing matter to fall farther inward, thus releasing potential energy and increasing the temperature of the gas. [175]

When the accreting object is a neutron star or a black hole, the gas in the inner accretion disk orbits at very high speeds because of its proximity to the compact object. The resulting friction is so significant that it heats the inner disk to temperatures at which it emits vast amounts of electromagnetic radiation (mainly X-rays). These bright X-ray sources may be detected by telescopes. This process of accretion is one of the most efficient energy-producing processes known up to 40% of the rest mass of the accreted material can be emitted as radiation. [175] (In nuclear fusion only about 0.7% of the rest mass will be emitted as energy.) In many cases, accretion disks are accompanied by relativistic jets that are emitted along the poles, which carry away much of the energy. The mechanism for the creation of these jets is currently not well understood, in part due to insufficient data. [176]

As such, many of the universe's more energetic phenomena have been attributed to the accretion of matter on black holes. In particular, active galactic nuclei and quasars are believed to be the accretion disks of supermassive black holes. [177] Similarly, X-ray binaries are generally accepted to be binary star systems in which one of the two stars is a compact object accreting matter from its companion. [177] It has also been suggested that some ultraluminous X-ray sources may be the accretion disks of intermediate-mass black holes. [178]

In November 2011 the first direct observation of a quasar accretion disk around a supermassive black hole was reported. [179] [180]

#### X-ray binaries

X-ray binaries are binary star systems that emit a majority of their radiation in the X-ray part of the spectrum. These X-ray emissions are generally thought to result when one of the stars (compact object) accretes matter from another (regular) star. The presence of an ordinary star in such a system provides an opportunity for studying the central object and to determine if it might be a black hole. [177]

If such a system emits signals that can be directly traced back to the compact object, it cannot be a black hole. The absence of such a signal does, however, not exclude the possibility that the compact object is a neutron star. By studying the companion star it is often possible to obtain the orbital parameters of the system and to obtain an estimate for the mass of the compact object. If this is much larger than the Tolman–Oppenheimer–Volkoff limit (the maximum mass a star can have without collapsing) then the object cannot be a neutron star and is generally expected to be a black hole. [177]

The first strong candidate for a black hole, Cygnus X-1, was discovered in this way by Charles Thomas Bolton, [181] Louise Webster, and Paul Murdin [182] in 1972. [183] [184] Some doubt, however, remained due to the uncertainties that result from the companion star being much heavier than the candidate black hole. Currently, better candidates for black holes are found in a class of X-ray binaries called soft X-ray transients. In this class of system, the companion star is of relatively low mass allowing for more accurate estimates of the black hole mass. Moreover, these systems actively emit X-rays for only several months once every 10–50 years. During the period of low X-ray emission (called quiescence), the accretion disk is extremely faint allowing detailed observation of the companion star during this period. One of the best such candidates is V404 Cygni. [177]

##### Quasi-periodic oscillations

The X-ray emissions from accretion disks sometimes flicker at certain frequencies. These signals are called quasi-periodic oscillations and are thought to be caused by material moving along the inner edge of the accretion disk (the innermost stable circular orbit). As such their frequency is linked to the mass of the compact object. They can thus be used as an alternative way to determine the mass of candidate black holes. [185]

#### Galactic nuclei

Astronomers use the term "active galaxy" to describe galaxies with unusual characteristics, such as unusual spectral line emission and very strong radio emission. Theoretical and observational studies have shown that the activity in these active galactic nuclei (AGN) may be explained by the presence of supermassive black holes, which can be millions of times more massive than stellar ones. The models of these AGN consist of a central black hole that may be millions or billions of times more massive than the Sun a disk of interstellar gas and dust called an accretion disk and two jets perpendicular to the accretion disk. [186] [187]

Although supermassive black holes are expected to be found in most AGN, only some galaxies' nuclei have been more carefully studied in attempts to both identify and measure the actual masses of the central supermassive black hole candidates. Some of the most notable galaxies with supermassive black hole candidates include the Andromeda Galaxy, M32, M87, NGC 3115, NGC 3377, NGC 4258, NGC 4889, NGC 1277, OJ 287, APM 08279+5255 and the Sombrero Galaxy. [189]

It is now widely accepted that the center of nearly every galaxy, not just active ones, contains a supermassive black hole. [190] The close observational correlation between the mass of this hole and the velocity dispersion of the host galaxy's bulge, known as the M–sigma relation, strongly suggests a connection between the formation of the black hole and that of the galaxy itself. [191]

### Microlensing (proposed)

Another way the black hole nature of an object may be tested in the future is through observation of effects caused by a strong gravitational field in their vicinity. One such effect is gravitational lensing: The deformation of spacetime around a massive object causes light rays to be deflected much as light passing through an optic lens. Observations have been made of weak gravitational lensing, in which light rays are deflected by only a few arcseconds. However, it has never been directly observed for a black hole. [193] One possibility for observing gravitational lensing by a black hole would be to observe stars in orbit around the black hole. There are several candidates for such an observation in orbit around Sagittarius A*. [193]

The evidence for stellar black holes strongly relies on the existence of an upper limit for the mass of a neutron star. The size of this limit heavily depends on the assumptions made about the properties of dense matter. New exotic phases of matter could push up this bound. [177] A phase of free quarks at high density might allow the existence of dense quark stars, [194] and some supersymmetric models predict the existence of Q stars. [195] Some extensions of the standard model posit the existence of preons as fundamental building blocks of quarks and leptons, which could hypothetically form preon stars. [196] These hypothetical models could potentially explain a number of observations of stellar black hole candidates. However, it can be shown from arguments in general relativity that any such object will have a maximum mass. [177]

Since the average density of a black hole inside its Schwarzschild radius is inversely proportional to the square of its mass, supermassive black holes are much less dense than stellar black holes (the average density of a 10 8 M black hole is comparable to that of water). [177] Consequently, the physics of matter forming a supermassive black hole is much better understood and the possible alternative explanations for supermassive black hole observations are much more mundane. For example, a supermassive black hole could be modelled by a large cluster of very dark objects. However, such alternatives are typically not stable enough to explain the supermassive black hole candidates. [177]

The evidence for the existence of stellar and supermassive black holes implies that in order for black holes to not form, general relativity must fail as a theory of gravity, perhaps due to the onset of quantum mechanical corrections. A much anticipated feature of a theory of quantum gravity is that it will not feature singularities or event horizons and thus black holes would not be real artifacts. [197] For example, in the fuzzball model based on string theory, the individual states of a black hole solution do not generally have an event horizon or singularity, but for a classical/semi-classical observer the statistical average of such states appears just as an ordinary black hole as deduced from general relativity. [198]

A few theoretical objects have been conjectured to match observations of astronomical black hole candidates identically or near-identically, but which function via a different mechanism. These include the gravastar, the black star, [199] and the dark-energy star. [200]

### Entropy and thermodynamics

In 1971, Hawking showed under general conditions [Note 5] that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and merge. [201] This result, now known as the second law of black hole mechanics, is remarkably similar to the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease. As with classical objects at absolute zero temperature, it was assumed that black holes had zero entropy. If this were the case, the second law of thermodynamics would be violated by entropy-laden matter entering a black hole, resulting in a decrease in the total entropy of the universe. Therefore, Bekenstein proposed that a black hole should have an entropy, and that it should be proportional to its horizon area. [202]

The link with the laws of thermodynamics was further strengthened by Hawking's discovery that quantum field theory predicts that a black hole radiates blackbody radiation at a constant temperature. This seemingly causes a violation of the second law of black hole mechanics, since the radiation will carry away energy from the black hole causing it to shrink. The radiation, however also carries away entropy, and it can be proven under general assumptions that the sum of the entropy of the matter surrounding a black hole and one quarter of the area of the horizon as measured in Planck units is in fact always increasing. This allows the formulation of the first law of black hole mechanics as an analogue of the first law of thermodynamics, with the mass acting as energy, the surface gravity as temperature and the area as entropy. [202]

One puzzling feature is that the entropy of a black hole scales with its area rather than with its volume, since entropy is normally an extensive quantity that scales linearly with the volume of the system. This odd property led Gerard 't Hooft and Leonard Susskind to propose the holographic principle, which suggests that anything that happens in a volume of spacetime can be described by data on the boundary of that volume. [203]

Although general relativity can be used to perform a semi-classical calculation of black hole entropy, this situation is theoretically unsatisfying. In statistical mechanics, entropy is understood as counting the number of microscopic configurations of a system that have the same macroscopic qualities (such as mass, charge, pressure, etc.). Without a satisfactory theory of quantum gravity, one cannot perform such a computation for black holes. Some progress has been made in various approaches to quantum gravity. In 1995, Andrew Strominger and Cumrun Vafa showed that counting the microstates of a specific supersymmetric black hole in string theory reproduced the Bekenstein–Hawking entropy. [204] Since then, similar results have been reported for different black holes both in string theory and in other approaches to quantum gravity like loop quantum gravity. [205]

Is physical information lost in black holes?

Because a black hole has only a few internal parameters, most of the information about the matter that went into forming the black hole is lost. Regardless of the type of matter which goes into a black hole, it appears that only information concerning the total mass, charge, and angular momentum are conserved. As long as black holes were thought to persist forever this information loss is not that problematic, as the information can be thought of as existing inside the black hole, inaccessible from the outside, but represented on the event horizon in accordance with the holographic principle. However, black holes slowly evaporate by emitting Hawking radiation. This radiation does not appear to carry any additional information about the matter that formed the black hole, meaning that this information appears to be gone forever. [206]

The question whether information is truly lost in black holes (the black hole information paradox) has divided the theoretical physics community (see Thorne–Hawking–Preskill bet). In quantum mechanics, loss of information corresponds to the violation of a property called unitarity, and it has been argued that loss of unitarity would also imply violation of conservation of energy, [207] though this has also been disputed. [208] Over recent years evidence has been building that indeed information and unitarity are preserved in a full quantum gravitational treatment of the problem. [209]

One attempt to resolve the black hole information paradox is known as black hole complementarity. In 2012, the "firewall paradox" was introduced with the goal of demonstrating that black hole complementarity fails to solve the information paradox. According to quantum field theory in curved spacetime, a single emission of Hawking radiation involves two mutually entangled particles. The outgoing particle escapes and is emitted as a quantum of Hawking radiation the infalling particle is swallowed by the black hole. Assume a black hole formed a finite time in the past and will fully evaporate away in some finite time in the future. Then, it will emit only a finite amount of information encoded within its Hawking radiation. According to research by physicists like Don Page [210] [211] and Leonard Susskind, there will eventually be a time by which an outgoing particle must be entangled with all the Hawking radiation the black hole has previously emitted. This seemingly creates a paradox: a principle called "monogamy of entanglement" requires that, like any quantum system, the outgoing particle cannot be fully entangled with two other systems at the same time yet here the outgoing particle appears to be entangled both with the infalling particle and, independently, with past Hawking radiation. [212] In order to resolve this contradiction, physicists may eventually be forced to give up one of three time-tested principles: Einstein's equivalence principle, unitarity, or local quantum field theory. One possible solution, which violates the equivalence principle, is that a "firewall" destroys incoming particles at the event horizon. [213] In general, which—if any—of these assumptions should be abandoned remains a topic of debate. [208]

## LIGO’s Biggest Mass Merger Ever Foretells A Black Hole Revolution

Two black holes, each with accretion disks, are illustrated here just before they collide. With the . [+] new announcement of GW190521, we discovered the heaviest mass black holes ever detected in gravitational waves, crossing the 100 solar mass threshold and revealing our first intermediate mass black hole.

Mark Myers, ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav).

After years of searching for gravitational waves, it finally happened: LIGO bagged the biggest one ever. Approximately 10 billion years ago, two massive black holes — weighing in at 85 and 66 times the mass of our Sun — merged together, converting approximately 8 solar masses into pure energy in the form of gravitational radiation. After journeying through the expanding Universe, those signals arrived at the National Science Foundation’s LIGO and the European Gravitational Observatory’s Virgo detectors, where they were detectable over a timespan of just

13 milliseconds. It was the most massive black hole merger ever detected.

It’s remarkable for a number of reasons, as it sets a slew of records, including:

• the most distant black hole-black hole merger (at 17 billion light-years away, accounting for the Universe’s expansion),
• the most massive progenitor black holes (at 85 and 66 solar masses),
• the most massive final black hole (at 142 solar masses),
• the greatest amount of mass turned into energy in a single event (8 solar masses),
• and the shortest-duration definitive signal ever seen (at

But the biggest surprise of all is that we didn’t expect these black holes to exist at all. Here’s the enormous puzzle presented by this new discovery, and the leading ideas on what the solution might be.

When the two arms are of exactly equal length and there is no gravitational wave passing through, . [+] the signal is null and the interference pattern is constant. As the arm lengths change, the signal is real and oscillatory, and the interference pattern changes with time in a predictable fashion.

The way gravitational wave detectors like LIGO actually “see” merging black holes is that these mergers create ripples in spacetime, where space alternately compresses and expands in two perpendicular directions, in phase, as the gravitational waves pass through them at the speed of light. By creating a detector where light travels repeatedly down-and-back along two long-baseline arms in perpendicular directions, those small and periodic distance changes can be seen, down to even a tiny fraction of a wavelength of the light used. Mirror displacements as small as

10 -19 meters can be detected.

### Mars, Venus And A ‘Super Solstice Strawberry Moon’ Sparkle In Twilight: What You Can See In The Night Sky This Week

But we can’t detect every source of gravitational waves in the Universe: only the ones that have both a sufficiently large amplitude (creating a large enough change in the relative positions of the mirrors) and that fall into a frequency range that the detectors are sensitive to (based on the physical size of the detector’s arms). Ground-based detectors like LIGO and Virgo are sensitive to mergers of collapsed objects — black holes and neutron stars — ranging from a few solar masses up to perhaps a few hundred solar masses.

The signal from the gravitational wave event GW190521, as seen in all three detectors. The entire . [+] signal duration lasted just

13 milliseconds, but represents the energy equivalent of 8 solar masses converted to pure energy via Einstein's E = mc^2.

R. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 125, 101102

This newest event, now officially known as GW190521, is the heaviest black hole-black hole merger ever seen. It’s so massive — and therefore, its event horizon is so large — that only the last couple of orbits before the merger could be seen by our terrestrial detectors. The “ringdown” phase, where the post-merger black hole settles down, could actually be detected as well, which provides a phenomenal amount of information to gravitational wave scientists about the properties of this merger. It really is this massive, this distant, and inconsistent with being anything other than two black holes merging together from nearly perfectly circularized orbits.

The post-merger black hole, at 142 solar masses, is also the very first “intermediate mass black hole” ever detected. We’ve detected stellar mass black holes before, which we loosely categorize as under 100 solar masses, which are assumed to form from massive stars that go supernova, experience a catastrophic instability, or otherwise collapse entirely. We’ve also detected supermassive black holes: of 100,000 solar masses or more, which live at the centers of massive galaxies. But for the in-between black holes, this is the first.

Two black holes of approximately equal mass, when they inspiral and merge, will exhibit the . [+] gravitational wave signal (in amplitude and frequency) shown at the bottom of the animation. The gravitational wave signal will spread out in all three dimensions at the speed of light, where it can be detected from billions of light-years away by a sufficient gravitational wave detector.

N. Fischer, H. Pfeiffer, A. Buonanno (Max Planck Institute for Gravitational Physics), Simulating eXtreme Spacetimes (SXS) Collaboration

Based on the black hole-black hole mergers already seen by LIGO and Virgo, we’d already learned an important lesson: 99% of black holes in binary, merging systems are below 43 solar masses. This is, at least so far, the first and only black hole-black hole merger we know about where both members are above that

43 solar mass threshold. It’s an important milestone for a vital reason: there must be some way to build up these supermassive black holes from smaller black holes, and that requires a population of these intermediate mass black holes. At last, we’ve discovered the very first one.

We know how the first one we’ve ever seen arose: from the merger of two lower-mass black holes. We don’t know if mergers, accretions, or some other mechanism (such as the direct collapse of material) is responsible for the majority of these intermediate mass black holes that must exist in the Universe, but at least we know how the first one came about. What we don’t know, however, is how we physically created at least one of the black holes — the 85 solar mass one — that led to its formation.

The anatomy of a very massive star throughout its life, culminating in a Type II Supernova. At the . [+] end of its life, if the core is massive enough, the formation of a black hole is absolutely unavoidable. In general, the more massive the progenitor star is, the more massive the black hole that results will be, but there is a "forbidden" range where black holes shouldn't exist.

Nicole Rager Fuller for the NSF

In theory, the lower-mass black holes are called “stellar mass” black holes because they arise as the remnants of stars, which live, die, and leave a black hole remnant behind. For all of the previous black holes seen by gravitational wave detectors, this explanation worked just fine, as the theoretical predictions for how massive stars died lined up with our observations of the black holes that existed.

But an 85 solar mass black hole? That, according to our best current understanding of stellar evolution, shouldn’t be possible.

Here’s why: if a star is massive enough to go supernova, it will form either a neutron star or a black hole, depending on its original mass. In general, the more massive a star is, the more massive the remnant it leads to. But this only works up to a point. Above a certain mass, the temperature inside the star gets so hot — above about 3 billion K — that the most energetic photons, which provide the radiation pressure that hold the star up against gravitational collapse, can spontaneously convert into matter-antimatter (electron-positron) pairs. This is a disaster for the star.

This diagram illustrates the pair production process that astronomers once thought triggered the . [+] hypernova event known as SN 2006gy. When high-enough-energy photons are produced, at temperature of 3 billion K or higher, they will create electron/positron pairs, causing a pressure drop and a runaway reaction that destroys the star. This event is known as a pair-instability supernova. Peak luminosities of a hypernova, also known as a superluminous supernova, are many times greater than that of any other, 'normal' supernova.

When this radiation spontaneously becomes matter and antimatter, it causes the radiation pressure inside the star to plummet, which lets gravitational collapse gain the upper hand. As a result of this collapse, the interior of the star gets even hotter: the same way that rapidly compressing a gas can cause it to heat up. This converts even more photons into electron-positron pairs, and this continues until a runaway fusion reaction is triggered in the star’s core, causing it to go supernova. Astrophysicists call this a “pair-instability supernova,” and it leads to the destruction of the entire star, with no remnant left behind.

Unfortunately, that should basically forbid the existence of stellar mass black holes in a certain mass range, and that range should definitely include an 85 solar mass black hole. The fact that LIGO and Virgo saw this merger with the properties they did indicates very strongly that — despite our theoretical expectations — black holes in this “forbidden” mass range really do exist. The big new question that arises as a result of this finding is simply: how?

Supernovae types as a function of initial star mass and initial content of elements heavier than . [+] Helium (metallicity). Note that the first stars occupy the bottom row of the chart, being metal-free, and that the black areas correspond to direct collapse black holes. For modern stars, we are uncertain as to whether the supernovae that create neutron stars are fundamentally the same or different than the ones that create black holes, and whether there is a 'mass gap' present between them in nature. A second mass gap should exist at higher masses.

Fulvio314 / Wikimedia Commons

1.) Our understanding of high-mass stellar interiors is incorrect. Maybe the pair-instability mechanism doesn’t work as we suspect. Maybe there’s some new physics we haven’t considered. Maybe neutrino production carries energy away and leads to black hole formation. Or maybe metallicity (the fraction of heavy elements in a star) can change this equation. It seems unlikely because the science is so theoretically well-understood, but we always have to consider that we might have something wrong.

2.) These black holes weren’t formed from stars, but are primordial: left over from the Big Bang itself. This is one of those extraordinarily unlikely scenarios with no evidence in favor of it, but not quite enough evidence to rule it out entirely. It’s possible that, in the early Universe, there were regions of space with more matter than average, and they collapsed directly to form black holes. That would require a region with

68% or more “extra” matter in it compared to the average the largest overdensities we know of are of

0.01% in magnitude. It’s not likely, but we can’t fully rule it out.

When a black hole and a companion star orbit one another, the star's motion will change over time . [+] owing to the gravitational influence of the black hole, while matter from the star can accrete onto the black hole, resulting in X-ray and radio emissions, as well as the growth of the black hole's mass.

Jingchuan YU/Beijing Planetarium/2019

3.) These black holes weren’t formed from the death of a single star. Now we’re starting to get into the realm of actual possibility here. We know that 50% of all stars form as a part of multi-star systems, and that a substantial fraction of stars (more than 10%) live in systems with 3, 4, 5, 6, or even 7 stars in them. (More are possible, but we haven’t found them yet.) If two or more stellar mass black holes merged together to create these progenitor black holes, which then merged in this event, there’s no problem at all. The biggest challenge to this scenario may be understanding why, when the earlier merger(s) occurred, the other members weren’t ejected in the process!

4.) These black holes grew after accreting mass from (or swallowing) a companion. They say that “might makes right” in warfare, and in astrophysics, a similar analogy is true. The highest-mass and highest-density clumps draw in the matter around them, and if these black holes formed with companions, some or even all of that matter could have been swallowed by the black hole after they formed. It’s a way for these black holes to grow to these higher masses without needing to form, immediately, with this supposedly forbidden mass values.

Two stellar mass black holes, if part of an accretion disk or flow around a supermassive black hole, . [+] can grow in mass, experience friction, and merge spectacularly, releasing a flare when they do. It's possible that GW190521 created such a flare when its two progenitor black holes merged, and that this configuration gave rise to that event.

5.) These black holes formed within the accretion disk around an active supermassive black hole. This is a wild scenario, but it may actually turn out to be correct. One of the places we know we’re likely to find black holes merging together is near the centers of galaxies, as matter often falls in towards the central black hole. These dense regions frequently have lots of new stars forming in them we see this even in our own galaxy. When a large amount of matter nears the central black hole, it can become active, creating an accretion disk, a region with a lot of drag, and “flares” when black holes merge together, either with one another or with the central black hole.

In an environment such as this, a black hole can easily accrete lots of mass, growing substantially in this environment. The 85 and 66 solar mass black holes may have been significantly smaller when they formed, having grown within the accretion disk. There is some exciting potential evidence for this, as an electromagnetic flare was seen coincident in time (and possibly in space) with this gravitational wave merger. Even if the observed flare is unrelated, this scenario still remains plausibly viable.

Here, 11 of the heaviest black hole-black hole mergers as discovered in gravitational waves are . [+] presented. With GW 190521, two black holes of 85 and 66 solar masses merged together, yielding a 142 solar mass black hole in the end: the first intermediate mass black hole ever directly and definitively detected.

In many ways, this is the best kind of science: an observation that surprises us, and compels us to rethink our theoretical assumptions in the process. We’ve just witnessed the heaviest black hole-black hole merger ever directly seen, and that led to the first definitive detection of an intermediate mass black hole of all. This event set a number of records, and ranks as the single most energetic event ever witnessed since the Big Bang: unleashing more than 100 times the energy of all the stars in the Universe over a brief period of

It also raises a number of spectacular questions. How did the black holes that gave rise to this intermediate mass one form? Do most intermediate mass black holes form this way, or from a different mechanism? Are these black holes currently embedded in the accretion disk of an active galaxy? Did they “flare” when they merged, and did we see it? Now that we’ve seen our first one, we can be certain these objects are out there. As additional observations take place and new data comes in, we can look forward to answering questions that, just a few short days ago, we didn’t even know we should be asking.

## This Is What We Know About Black Holes In Advance Of The Event Horizon Telescope's First Image

An illustration of heavily-curved spacetime, outside the event horizon of a black hole. As you get . [+] closer and closer to the mass's location, space becomes more severely curved, eventually leading to a location from within which even light cannot escape: the event horizon. The radius of that location is set by the mass of the black hole, the speed of light, and the laws of General Relativity alone.

Pixabay user JohnsonMartin

For hundreds of years, physicists have hypothesized that the Universe should contain black holes. If enough matter is gathered into a small enough volume of space, the gravitational pull will be so strong that nothing in the Universe — no particles, no antiparticles, not even light itself — can escape. They are predicted by both Newton's and Einstein's theories of gravity, and astrophysicists have observed many candidate objects that are consistent with black holes and no other explanations.

But we've never seen the event horizon before: the characteristic signature unique to black holes, of the dark region where nothing can escape. On April 10, 2019, the Event Horizon Telescope collaboration will release their first-ever image of such an event horizon. Here's what we know right now, on the eve of this monumental discovery.

The black hole at the center of the Milky Way, along with the actual, physical size of the Event . [+] Horizon pictured in white. The visual extent of darkness will appear to be 250-300% as large as the event horizon itself.

Ute Kraus, Physics education group Kraus, Universität Hildesheim background: Axel Mellinger

Black holes are an inevitable consequence, at least in theory, of having a speed limit in your Universe. Einstein's theory of General Relativity, which relates the fabric of spacetime to the matter and energy present within the Universe, also contains a built-in relationship between how matter and energy move through spacetime. The greater your motion through space, the lesser your motion through time, and vice versa.

But there's a constant relating that motion: the speed of light. In General Relativity, the physical size of the predicted event horizon — the size of the region from which nothing can escape — is set by the mass of the black hole and the speed of light. If the speed of light were faster-or-slower, the predicted size of the event horizon would shrink-or-grow, respectively. If light moved infinitely fast, there would be no event horizon at all.

LIGO and Virgo have discovered a new population of black holes with masses that are larger than what . [+] had been seen before with X-ray studies alone (purple). This plot shows the masses of all ten confident binary black hole mergers detected by LIGO/Virgo (blue), along with the one neutron star-neutron star merger seen (orange). LIGO/Virgo, with the upgrade in sensitivity, should detect multiple mergers every week beginning this April.

LIGO/VIrgo/Northwestern Univ./Frank Elavsky

Astrophysically, black holes are surprisingly easy to create. Within our Milky Way galaxy alone, there are likely hundreds of millions of black holes. At present, we believe there are three mechanisms capable of forming them, although there may be more.

1. The death of a massive star, where the core of a star much heavier than our Sun, rich in heavy elements, collapses under its own gravity. When there's insufficient outward pressure to counteract the inward gravitational force, the core implodes. The resulting supernova explosion leads to a central black hole.

The visible/near-IR photos from Hubble show a massive star, about 25 times the mass of the Sun, that . [+] has winked out of existence, with no supernova or other explanation. Direct collapse is the only reasonable candidate explanation.

2. The direct collapse of a large amount of matter, which could either arise from a star or a cloud of gas. If enough matter is present in a single location in space, it can generate a black hole directly, without a supernova or similar cataclysm to trigger its creation.

3. The collision of two neutrons stars, which are the most dense, massive objects which do not become black holes. Add enough mass onto one, either through accretion or (more commonly) mergers, and a black hole can arise.

Artist’s illustration of two merging neutron stars. The rippling spacetime grid represents . [+] gravitational waves emitted from the collision, while the narrow beams are the jets of gamma rays that shoot out just seconds after the gravitational waves (detected as a gamma-ray burst by astronomers). The aftermath of the neutron star merger observed in 2017 points towards the creation of a black hole.

NSF / LIGO / Sonoma State University / A. Simonnet

A little more than 0.1% of the stars that have ever been formed in the Universe will eventually become black holes in one of these fashions. Some of these black holes will be only a few times the mass of our Sun others can be hundreds or even thousands of times as massive.

But the more massive ones will do what all extremely massive objects do when they move through the gravitational collection of masses typical to star clusters and galaxies: they will sink to the center, through the astronomical process of mass segregation. When multiple masses swarm around in a gravitational potential well, the lighter masses tend to pick up more momentum and potentially get ejected, while the larger ones lose angular momentum and collect in the center. There, they can accrete matter, merge, grow, and eventually become the supermassive behemoths we find today at the centers of galaxies.

The supermassive black hole at the center of our galaxy, Sagittarius A*, flares brightly in X-rays . [+] whenever matter is devoured. In other wavelengths of light, from infrared to radio, we can see the individual stars in this innermost portion of the galaxy.

X-ray: NASA/UMass/D.Wang et al., IR: NASA/STScI

Additionally, black holes don't exist in isolation, but in the messy environment of space itself, which is filled with matter of various types. When matter gets close to a black hole, there will be tidal forces on it. The part of any object that happens to be closer to the black hole experiences a larger gravitational force than the part farther away from the black hole, while the portions that bulge on any of the sides will feel a pinch towards the center of the object.

All told, this results in a set of stretching forces in one direction and compressing forces along the perpendicular directions, causing the infalling object to "spaghettify." The object will be torn apart into its constituent particles. Owing to a number of physical properties and dynamics at play, this will cause matter to accrue around the black hole in a disk-like shape: an accretion disk.

An illustration of an active black hole, one that accretes matter and accelerates a portion of it . [+] outwards in two perpendicular jets, is an outstanding descriptor of how quasars work. The matter that falls into a black hole, of any variety, will be responsible for additional growth in both mass and size for the black hole. Despite all the misconceptions out there, however, there is no 'sucking in' of external matter.

These particles making up the disk are charged, and move in orbit around the black hole. When charged particles move, they create magnetic fields, and magnetic fields in turn accelerate charged particles. This should result in a number of observable phenomena, including:

• emitted photons from throughout the electromagnetic spectrum, particularly in the radio,
• flares that show up at higher energies (such as in the X-ray) arising from when matter falls into the black hole,
• and jets of both matter and antimatter that get accelerated perpendicular to the accretion disk itself.

All of these phenemona have been seen for black holes of various masses and orientations, further giving credence to their existence.

A large slew of stars have been detected near the supermassive black hole at the Milky Way's core. . [+] In addition to these stars and the gas and dust we find, we anticipate there to be upwards of 10,000 black holes within just a few light years of Sagittarius A*, but detecting them had proved elusive until earlier in 2018. Resolving the central black hole is a task that only the Event Horizon Telescope can rise to, and may yet detect its motion over time.

S. Sakai / A. Ghez / W.M. Keck Observatory / UCLA Galactic Center Group

In addition, we've observed the motions of individual stars and stellar remnants around black hole candidates, which appear to orbit large masses that have no viable explanations other than being black holes. In the center of the Milky Way, for example, we have observed dozens of stars orbiting an object known as Sagittarius A*, which has an inferred mass of 4 million Suns and emits flares, radio waves, and shows signatures of positrons (a form of antimatter) being ejected perpendicular to the galactic plane.

Other black holes show many of the same signatures, such as the ultramassive black hole at the center of the galaxy M87, which is estimated to weigh in at 6.6 billion solar masses.

The second-largest black hole as seen from Earth, the one at the center of the galaxy M87, is shown . [+] in three views here. Despite its mass of 6.6 billion Suns, it is over 2000 times farther away than Sagittarius A*. It may or may not be resolvable by the EHT, but if the Universe is kind, we'll not only get an image, but learn whether the X-ray emissions give us accurate mass estimates for black holes or not.

Top, optical, Hubble Space Telescope / NASA / Wikisky lower left, radio, NRAO / Very Large Array (VLA) lower right, X-ray, NASA / Chandra X-ray telescope

Finally, we've seen a slew of other observational signatures, such as the direct detection of gravitational waves from inspiraling and merging black holes, the creation of a black hole directly from both direct collapse events and neutron star mergers, and the turning on-and-off of quasars, blazars, and microquasars, which are thought to be caused by black holes of varying masses and orientations.

Going into the Event Horizon Telescope's big reveal, we have every reason to believe that black holes exist, are consistent with General Relativity, and are surrounded by matter, which accelerates and emits radiation that we should be able to detect.

Artist's impression of an active galactic nucleus. The supermassive black hole at the center of the . [+] accretion disk sends a narrow high-energy jet of matter into space, perpendicular to the disc. A blazar about 4 billion light years away is the origin of many of the highest-energy cosmic rays and neutrinos. Only matter from outside the black hole can leave the black hole matter from inside the event horizon can never escape.

DESY, Science Communication Lab

The big advance of the Event Horizon Telescope will be the ability to finally resolve the event horizon itself. From within that region, no matter should exist, and no radiation should be emitted. There should be subtle effects intrinsic to black holes themselves that are observable with this telescope, including the fact that the innermost stable circular orbit should be about three times the size of the event horizon itself, and radiation ought to be emitted from around the event horizon, owing to the presence of accelerated matter.

There are many questions that the first direct image of a black hole's event horizon should be poised to answer, and you can check out what we can potentially learn here. But the biggest advance is this: it will test General Relativity's predictions in an entirely new way. If our understanding of gravity needs to be revised close to black holes, this observation will show us the way.

Two of the possible models that can successfully fit the Event Horizon Telescope data thus far, as . [+] of early 2018. Both show an off-center, asymmetric event horizon that's enlarged versus the Schwarzschild radius, consistent with the predictions of Einstein's General Relativity. A full image has not yet been released to the general public, but is expected on April 10, 2019.

For hundreds of years, humanity has expected black holes to exist. Over the course of all of our lifetimes, we've collected an entire suite of evidence that points not only to their existence, but to a fantastic agreement between their expected theoretical properties and what we've observed. But perhaps the most important prediction of all — that of the event horizon's existence and properties — has never been directly tested before.

With simultaneous observations in hand from hundreds of telescopes across the globe, scientists have finished reconstructing an image, based on real data, of the largest black hole as seen from Earth: the 4 million solar mass monster at the center of the Milky Way. What we'll see on April 10 will either further confirm General Relativity or cause us to rethink all that we believe about gravity. Eager with anticipation, the world now awaits.

## Black hole

Cygnus X-1 was discovered by X-ray instruments that were carried by a sounding rocket launched in New Mexico, from White Sands Missile Range. A survey was conducted in 1964 to map the X-ray sources using two Aerobee suborbital rockets that carried Geiger counters to measure the emissions. Cygnus X-1 was one of the eight X-ray sources discovered during the survey.

Evidence for the existence of black holes – both stellar mass black holes like Cygnus X-1 and supermassive black holes like Sagittarius A*, which are about a million times heavier and found at the centres of galaxies – has been found in the last 50 years or so, but at the time Cygnus X-1 was discovered, they were still considered hypothetical objects. Black holes can’t be observed directly, which means that proving their existence is difficult. The strongest evidence comes from binary systems like Cygnus X-1/HD 226868 or V404 Cygni, in which a star that can be observed is seen orbiting a massive but invisible companion.

In 1970, NASA launched the Uhuru satellite, which detected 300 new X-ray sources and revealed new information about Cygnus X-1. The Uhuru observations showed fluctuations in intensity of the X-ray emissions occurring several times a second. This meant that the energy was generated over a region of approximately 105 kilometres, which was relatively small.

The X-ray source was pinpointed to the star HDE 226868 in April and May 1971, when astronomers at Leiden Observatory and the National Radio Astronomy Observatory made independent observations of the system. The star, a supergiant, is located about half a degree from Eta Cygni. As the star is not capable of emitting such quantities of X-rays, scientists theorized that it had to have a companion that was capable of heating gas to the extreme temperatures needed to generate the emissions.

Cygnus X-1, image: NASA/CXC/M.Weiss

A massive hidden companion to the supergiant was discovered the same year by astronomers at the Royal Greenwich Observatory and the David Dunlap Observatory at the University of Toronto. The companion was detected by measuring the Doppler shift of the supergiant star’s spectrum. As the companion’s mass, estimated from orbital parameters, was extremely high, the object was taken to be a black hole, because the alternative – a neutron star – could not have a mass more than three times that of the Sun, which the companion did. (The consensus on neutron stars is that they can’t have more than three solar masses.) Additionally, neutron stars typically exhibit pulsations with a stable period, and these have never been detected from Cygnus X-1. Also, measurements of the motion of Cygnus X-1 through space revealed that it was moving quite slowly with respect to the Milky Way, suggesting that it was not created in a supernova explosion: it did not get that much of a kick when it was born. If it had, it would travel faster through the Milky Way. The progenitor star remained in orbit, which suggests that it did not explode as a supernova because it would have likely been ejected from the star system at a high speed. As it stayed in orbit, this indicates that it may have collapsed directly into a black hole or only had a modest explosion. After further observations strenghtened the black hole theory, Cygnus X-1 was widely accepted to be one by the end of 1973.

In 1992, the High Speed Photometer on the Hubble Space Telescope may have detected evidence of an event horizon around Cygnus X-1, when it recorded two final bursts of energy from material passing through what is presumably the event horizon.

In 2006, Cygnus X-1 became the first candidate for a stellar mass black hole to show evidence of gamma ray emission in the high energy band.

Cygnus X-1
Constellation: Cygnus
Location: 19h 58m 21.67595s (right ascension), +35°12󈧉.7783 (declination)
Spectral class: O9.7Iab
Visual magnitude: 8.95
Absolute magnitude: −6.5±0.2
Mass 14-16 solar masses
Temperature: 31,000 K
Age: 5 million years
Distance: 6,100 ± 400 light years (1,900 ± 100 parsecs)
Designations: Cygnus X-1, Cyg X-1, V1357 Cyg, SAO 69181, HIP 98298, HD(E) 226868, BD+34 3815, AG(K2)+35 1910

## A Black Hole Primer with Chandra

The Event Horizon Telescope (EHT), a network of radio antennae around the globe, has captured the first image of a black hole event horizon. This black hole is located in Messier 87, or M87, which is about 60 million light years from Earth. Chandra has studied M87 many times over its 20-year mission and sees a much wider field-of-view than the EHT. The "+" marks the spot in the Chandra image on the left for the location of the EHT image on the right (not to same scale) Credit: Left: NASA/CXC/SAO Right: Event Horizon Telescope Collaboration. MORE

### The Basics

What is a black hole?
When a star runs out of nuclear fuel, it will collapse. If the core, or central region, of the star has a mass that is greater than three Suns, no known nuclear forces can prevent the core from forming a deep gravitational warp in space called a black hole.

A black hole does not have a surface in the usual sense of the word. There is simply a region, or boundary, in space around a black hole beyond which we cannot see. This boundary is called the event horizon. The radius of the event horizon (proportional to the mass) is very small, only 30 kilometers for a non-spinning black hole with the mass of 10 Suns.

Anything that passes beyond the event horizon is doomed to be crushed as it descends ever deeper into the gravitational well of the black hole. No visible light, nor X-rays, nor any other form of electromagnetic radiation, nor any particle, no matter how energetic, can escape.

Did you know?
The center of our Milky Way galaxy contains a giant black hole with the mass equivalent to about 4 million Suns or about 3x10 36 kg

Anatomy of a Supermassive Black Hole:
Supermassive black holes with the mass of many millions of stars are thought to lie at the center of most large galaxies. The evidence comes from optical and radio observations which show a sharp rise in the velocities of stars or gas clouds orbiting the centers of galaxies. High orbital velocities mean that something massive is creating a powerful gravitational field which is accelerating the stars. X-ray observations indicate that a large amount of energy is produced in the centers of many galaxies, presumably by the in-fall of matter into a black hole.

Illustration: ESO, ESA/Hubble, M.Kornmesser/N.Bartmann Labels: NASA/CXC

accretion disk A disk of gas and dust that can accumulate around a center of gravitational attraction, such as a normal star, a white dwarf, neutron star, or black hole. As the gas spirals in due to friction, it becomes hot and emits radiation.

event horizon Imaginary spherical surface surrounding a black hole, with radius equal to the Schwarzschild radius, within which no event can be seen heard, or known about by an outside observer.

singularity A point in the universe where the density of matter and the gravitational field are infinite, as in the center of a black hole.

relativistic jet A powerful jet of radiation and particles traveling close to the speed of light.

### Chandra, Black Hole Hunter

With its unique properties, Chandra is peerless as a black hole probe—both near and far. Chandra can’t “see” into black holes, but it can tackle many of their mysteries. Using Chandra, scientists have found evidence for mid-sized black holes, found hidden populations, and estimated how many black holes are in the Universe. They have studied their dining habits and how fast they spin. They found a black hole that generated the deepest note ever detected in the Universe, and another that generated the most powerful explosion. They found direct evidence for a star that was torn apart by a supermassive black hole. They observed two supermassive black holes orbiting in the same galaxy, destined for a titanic collision. Chandra observations strongly confirmed the reality of the "event horizon".

Some of Chandra's findings on supermassive black holes were expected, while others were unexpected! A few highlights include:

EXPECTED AND DETECTED:
Thousands of supermassive black holes. These black holes are located in the centers of galaxies and Chandra has shown they exhibit a wide range of sizes and levels of explosive activity. MORE

UNEXPECTED:
Finding a black hole a million times more massive than the Sun in a star-forming dwarf galaxy is a strong indication that supermassive black holes can form more quickly than the galaxy they reside in. This has implications for understanding the formation of galaxies and black holes in the early universe. MORE

UNEXPECTED:
A Chandra survey of nine galaxies shows that most of the energy released by matter falling toward supermassive black holes in these galaxies is in the form of high-energy jets traveling at near the speed of light away from the black hole. MORE

UNEXPECTED:
Chandra images have revealed that many galaxies have jets of high-energy particles that extend to the outer reaches of the galaxy and affect the appearance and evolution of these galaxies. These jets are generated by matter falling toward supermassive black holes in the centers of the galaxies. MORE

Expect more startling revelations about the lives of black holes as Chandra continues its mission to explore our Universe.

One of the most important black holes to study is the one found at the center of our Milky Way galaxy. Known as Sagittarius A*, this black hole is about 4 million times the mass of the Sun and Chandra has revealed much about its behavior and history. MORE

Galaxies can merge and when they do, the supermassive black holes at their centers may also collide. This is the case of NGC 6240 where Chandra finds two giant black holes—the bright point-like sources in this middle of the image—are only 3,000 light years apart. MORE

The galaxy Centaurus A is well known for a spectacular jet of outflowing material - seen pointing from the middle to the upper left in this Chandra image - that is generated by a giant black hole at the galaxy's center. Chandra has also revealed information about smaller black holes throughout Centaurus A. MORE

### Black holes: Questions & Answers

How are black holes created? In general, black holes are created whenever enough matter is squeezed into a small enough space. To turn the Earth into a black hole, we would have to compress all its mass into a region the size of a marble! Stellar mass black holes are formed when a massive star (more than about 25 times the mass of our Sun) runs out of fuel and its core collapses. The formation of supermassive black holes is more mysterious. They may be created when stellar mass black holes merge and gobble up matter in their vicinity, or by the collapse of giant clouds of dust and gas.

Can X-ray telescopes see a black hole? No light of any kind, including X-rays, can escape from inside the event horizon of a black hole. The X-rays Chandra observes from the vicinity of black holes are from matter that is close to the event horizon of black holes. Matter is heated to millions of degrees as it is pulled toward the black hole, so it glows in X-rays.

How do you find black holes with Chandra if you can't see them? Searching for black holes is a tricky business. One way to locate black holes is to search for the X-radiation from a disk of hot gas swirling toward a black hole. Friction between particles in the disk heats them to many millions of degrees, and they produce X-rays. Such disks have been found in binary star systems composed of a normal star in a close orbit around a stellar-mass black hole and, on a much larger scale, around the supermassive black holes in the centers of galaxies.

What happens to objects when they get too close to a black hole? Objects can orbit a black hole without any serious consequences as long as the size of their orbit is much greater than the diameter of the event horizon of a black hole, which is about 30 kilometers for a stellar black hole, and many millions of kilometers for a supermassive black hole. But, if any object gets too close, its orbit will become unstable and the object will fall into the black hole.

Is all matter in the disk around a black hole doomed to fall into the black hole? No, sometimes gas will escape as a hot wind that is blown away from the disk at high speeds. Even more dramatic are the high-energy jets that X-ray and radio observations show exploding away from the vicinity of some supermassive black holes. These jets can move at nearly the speed of light in tight beams and can travel hundreds of thousands of light years.

Do black holes grow when matter falls into them? Yes, the mass of the black hole increases by the amount of mass that was captured. For a stellar-mass black hole the radius of the event horizon increases by about 3 kilometers for every solar mass that is captured.

Are there limits to black hole growth? Theoretically, black holes can grow without limit. However, in the Universe, black holes do not have an infinite food supply! Sooner or later they will consume all the matter within their gravitational reach. Material further away may be affected by the gravitational field of the black hole, as we on Earth are affected by the massive black hole in the center of the Milky Way, but will not fall past its event horizon.

Can matter ever come back out of a black hole? No, even if matter was able to move at the speed of light, it could not escape once it falls past the event horizon. This is because the gravitational field inside a black hole is so strong that space is curved in on itself. Anything that falls into a black hole is able to travel in one direction only—towards the singularity (a point of infinite density where the laws of physics as we know them break down) at the center. Stephen Hawking showed that quantum theory implies that black holes should emit radiation. This radiation is predicted to be exceedingly weak and undetectable, except for hypothetical black holes with the mass less than that of a comet, and has yet to be observed.

## Astronomy (USA): what is the size of a black hole?

Somewhere in the center of the milky Way lurks a giant black hole, whose mass is several million times the mass of the Sun. Like all black holes, supermassive this giant called “Sagittarius a*” (abbreviated to Sgr A*, pronounced “Sagittarius a star” — approx. transl.) absorbs everything that comes within the scope of its gravitational field — this giant devours everything, including light. However, the absorption of matter is just one of the ways by which these cosmic monsters grow to truly astronomical proportions, gaining a mind-blowing mass. Note that describing a black hole as a giant space objects, astronomers usually have in mind its huge mass, not the size.

And here a logical question arises: what are the different sizes of black holes?

Distribution black holes is by class depending on weight

A normal black hole (known as the “black hole of stellar mass”) is formed when the evolutionary cycle of a massive star, the weight of which exceeds almost 8 solar masses, is about to end. After burning down the remains of nuclear fuel, the phase of rapid gravitational contraction (or gravitational collapse) of a star, then there is a giant explosion, — so there is a supernova. And what is left will become either a neutron star or a black hole depending on the mass of the star. The mass of such black holes can range from a couple to several tens of solar masses.

However, the question of the origin of superheavy black holes, such as “Sagittarius a*”, which are millions and even billions of times greater than the mass of the Sun remains unresolved. Astronomers know that a giant the size and mass of such black holes, seem to be associated with galaxies related communication, and the biggest of superheavy black holes was discovered in the centers of most large galaxies.

These arguments and recent evidence of the existence of a theoretically predicted class of black holes of medium size (they are called black holes the average weight that varies from hundred to one million solar masses), seem to indicate that black holes may be the supermassive after countless black holes of stellar mass and intermediate mass through billions of years will merge together.

It is clear that different types of black holes vary greatly in weight, and yet, not entirely clear how they differ in size.

What if the earth and the Sun were once black holes?

To examine the sizes of black holes, let us first consider the two most studied object — the Earth and the Sun.

The mass of the Earth is about 6×1024 kg And although from the standpoint of the layman is a huge figure, it is still negligible compared to the mass of the black hole.

Below appeared a black hole, it is necessary to concentrate a large enough mass, and its gravitational pull should be so strong that no other force will be able to prevent gravitational collapse of the mass. That’s why scientists have been unable to find black holes as light as the Earth, these space objects just did not have enough mass for gravitational compression. (But some scholars believe that in the first few moments after the Big Bang could appear ancient class of so-called primary black holes. The mass of these hypothetical objects might vary from very small to huge, in the tens of thousands of times the mass of the Sun.)

It is believed that in the center of a black hole is a bottomless gravitational pit of space-time, called gravitational singularity. The density of the singularity is infinite, and all that gets there stays there forever. The outer edge of a black hole is called the event horizon it represents the boundary beyond which it can not escape, no particle of matter trapped in the gravitational field of a black hole, including light quanta. The radius of the event horizon depends on the mass of the black hole the radius was first calculated by the German astronomer Karl Schwarzschild (Schwarzschild, Karl) in 1916.

For a black hole with a mass comparable to the mass of the Earth, the Schwarzschild radius is less than one inch (2.54 cm) — that is, the size of a ball for table tennis. For the Sun the Schwarzschild radius will be slightly less than two miles (3.2 km).

What are the smallest known black holes?

As we know, black holes are very difficult to detect. And because, unlike stars, they don’t glow, because the light photons will never escape beyond the event horizon. However, sometimes appears a black hole accretion disk — halo of matter moving around a black hole however, due to friction between the layers of this substance occurs glow. Scientists are able to observe a black hole only by the light emitted by the accretion disk otherwise, a black hole is invisible. In addition, the black hole can be detected by the impact it has on other space objects. For example, the scientists found the object of “Sagittarius a*” only after it was fixed the weirdness in the behavior of seven stars revolving around it.

Using these methods, scientists in recent years have found numerous candidates for the role of the black hole, including the smallest known to us the black hole, located in a binary system GRO J1655-40. Gas from the visible star in this system, flows to the black hole, generating sufficient energy flux to power microquasar.

Quasars evolve in an extremely bright active galactic nuclei (the centers of galaxies), which is a supermassive black hole surrounded by a bright and powerful accretion disk. According to some estimates, the black hole in GRO J1655-40 weighs about 5.4 times greater than the Sun, and its radius is about 10 miles (16 km). By studying microquasars such, astronomers hope to better understand the possible link between giants, hidden in the cores of galaxies, and a small excretiruemami black holes scattered throughout the galaxies.

In 2008, scientists at first concluded that they had discovered a black hole even smaller, but later the same researchers the mass of this space object has been adjusted. Any black hole smaller could appear, most likely, the merger of two neutron stars, and not the result of a gravitational collapse of a dying star. Laser interferometric gravitational-wave Observatory (LIGO) detects gravitational waves from mergers of neutron stars in 2017, just two years after the gravitational waves were actually discovered for the first time. Gravitational waves emitted during the mergers, give scientists a new way to identify black holes in a radius of 100 million light years from Earth.

On the other hand, the size of a black hole of stellar mass depends on how massive the star was, she was preceded. The heavy star, which has been found to date, denoted by the acronym R136a1, it weighs 315 times greater than the Sun. A black hole with the same mass, resulting from it as a result of gravitational collapse, would have a radius of about 578 miles (930,2 km). Despite its large size (compared to the smallest known black holes), even this huge black hole of stellar mass is nothing in comparison with their supermassive cousins.

How big are black holes of intermediate mass?

Between black holes of stellar mass and supermassive black holes are the so-called black holes of intermediate mass — that is, the long-awaited “missing link” in the evolution of a black hole. To date, only a few candidates for the role of this level, including space object found by the Hubble telescope earlier this year. These objects are even harder to find because they are less active in the absence of close space objects, which serve as a kind of “fuel”.

The mass of the black hole, recently discovered by Hubble in 50 thousand times the mass of the Sun. It is in a remote and dense star cluster, located on the outskirts of the galaxy large size, this is where astronomers expected to find evidence of these “missing links”. A candidate for the role of black holes of intermediate masses will be in the tens of thousands of times heavier than the Sun, and its radius will be one-fifth of the Sun’s radius, or about twice the radius of Jupiter.

Although black holes of intermediate masses have considerable size, their weight ranges from 100 to 100 thousand solar masses. Meanwhile the mass of the super-heavy black holes may be billions of times greater than the sun.

Measure the dimensions of superheavy black holes

From the Central black hole of our galaxy, “Sagittarius A*”, located 26 thousand light years from the Sun, the radius is about 17 times solar, and this means that the size of this black hole is limited, for example, the orbit of mercury. Although we mentioned the black hole in the milky Way weighs about 4 million solar masses, its dimensions are small in comparison to some other supermassive black holes that lurk at the center of other galaxies.

The largest of the supermassive black holes found to date is in the cluster of galaxies Abell 85. In the center of this cluster, located galaxy Holm 15A, where the total mass of the substance centered there is about 2 trillion solar masses. The centre of this galaxy is almost as large as the Large Magellanic Cloud, the radius of which is 7000 light years.

This star cluster is located at a distance of 700 million light years from Earth, its dimensions are twice the dimensions of any of the previous black holes. It was installed after began to receive information from the Observatory on the mountain Wendelstein at the University. Ludwig and Maximilian and from the telescope VLT (Very Large Telescope “Very large telescope”) ESO. Scientists have discovered that the black hole at the center of the galaxy Holm 15A has an enormous mass of 40 billion solar masses, or about two-thirds of the mass of all stars in the milky Way. With such a huge mass it has a diameter comparable to the diameter of the Solar system — generally this is an unprecedented size for any single object.

But the size of the observable Universe is 46.5 billion light years in all directions, which means that astronomers make the first steps in understanding the nature of black holes. Only a year ago with a telescope Event Horizon Telescope (Telescope the event horizon), which consists of eight telescopes located in different parts of the Earth, for the first time managed to image the black hole. In addition, it is expected that the observatories LIGO and Virgo, gravitational waves learners will be able annually to detect thanks to new technologies, about 40 mergers of double stars, and open black holes and neutron stars, located in the neighborhood of such stars. In addition, due to the more advanced telescopes, such as Space telescope NASA’s James Webb (James Webb Space Telescope, JWST) and Extremely large telescope (Extremely Large Telescope, ELT) of the European space Agency that will receive the first images within the next decade, it is difficult to predict how all black holes — those space monsters will be discovered in the future in the dark depths of space.

## Are Black Holes Falsifiable?

Things cannot be judged falsifiable or non-falsifiable. The concept of being falsifiable only applies to theories or hypotheses. One can't say the unicorns are falsifiable, but the hypothesis "there are no unicorns" is. The imagined experiment would consist of finding a unicorn. If one were found, the hypothesis would be refuted. None has ever been found, but that's not germane to the question of falsifiability. Similarly, the hypothesis "there are no black holes" is falsifiable. The test would be to find one. (Many have been found, perhaps the most notable being the ones involved in the discovery of gravitational waves.)

1. Willaperht

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2. Liviu

3. Yerodin

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5. Westcott

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