BLACK HOLE 2 (publishes)
Event horizon
Main article: Event horizon
 Far away from the black hole, a particle can move in any direction, as illustrated by the set of arrows. It is only restricted by the speed of light. |
 Closer to the black hole, spacetime starts to deform. There are more paths going towards the black hole than paths moving away.[Note 1] |
 Inside of the event horizon, all paths bring the particle closer to the center of the black hole. It is no longer possible for the particle to escape. |
The defining feature of a black hole is the appearance of an event horizon—a boundary in spacetime through which matter and light can only pass inward towards the mass of the black hole. Nothing, not even light, can escape from inside the event horizon. 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 if such an event occurred.[45]
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.[46] 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.
To a distant observer, clocks near a black hole appear to tick more slowly than those further away from the black hole.[47] Due to this effect, known as gravitational time dilation, an object falling into a black hole appears to slow down as it approaches the event horizon, taking an infinite time to reach it.[48] At the same time, all processes on this object slow down, for a fixed outside observer, causing emitted light to appear redder and dimmer, an effect known as gravitational redshift.[49] Eventually, at a point just before it reaches the event horizon, the falling object becomes so dim that it can no longer be seen.
On the other hand, an observer falling into a black hole does not notice any of these effects as he crosses the event horizon. According to his own clock, he crosses the event horizon after a finite time without noting any singular behaviour. In particular, he is unable to determine exactly when he crosses it, as it is impossible to determine the location of the event horizon from local observations.[50]
The shape of the event horizon of a black hole is always approximately spherical.[Note 2][53] For non-rotating (static) black holes the geometry is precisely spherical, while for rotating black holes the sphere is somewhat oblate.
Singularity
Main article: Gravitational singularity
At the center of a black hole as described by general relativity lies a gravitational singularity, a region where the spacetime curvature becomes infinite.[54] 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 lying in the plane of rotation.[55] 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.[56] The singular region can thus be thought of as having infinite density.
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 point; after attaining a certain ideal velocity, it is best to free fall the rest of the way.[57] 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".[58]
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.[59] The possibility of traveling to another universe is however only theoretical, since any perturbation will destroy this possibility.[60] It also appears to be possible to follow closed timelike curves (going back to one's own past) around the Kerr singularity, which lead to problems with causality like the grandfather paradox.[61] It is expected that none of these peculiar effects would survive in a proper quantum treatment of rotating and charged black holes.[62]
The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory.[63] 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.[64][65]
Photon sphere
Main article: Photon sphere
The photon sphere is a spherical boundary of zero thickness such that photons moving along tangents to the sphere will be trapped in a circular orbit. For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. The orbits are dynamically unstable, hence any small perturbation (such as a particle of infalling matter) will grow over time, either setting it on an outward trajectory escaping the black hole or on an inward spiral eventually crossing the event horizon.[66]
While light can still escape from inside the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light reaching an outside observer from inside the photon sphere must have been emitted by objects inside the photon sphere but still outside of the event horizon.[66]
Other compact objects, such as neutron stars, can also have photon spheres.[67] This follows from the fact that the gravitational field of an object does not depend on its actual size, hence any object that is smaller than 1.5 times the Schwarzschild radius corresponding to its mass will indeed have a photon sphere.
Ergosphere
Main article: 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 becomes 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.[68]
The ergosphere of a black hole is bounded by the (outer) event horizon on the inside and an oblate spheroid, which coincides with the event horizon at the poles and is noticeably wider around the equator. The outer boundary is sometimes called the ergosurface.
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. This energy is taken from the rotational energy of the black hole causing it to slow down.[69]
Formation and evolution
Considering the exotic nature of black holes, it may be natural to question if such bizarre objects could exist in nature or to suggest that they are merely pathological solutions to Einstein's equations. Einstein himself wrongly thought that black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius.[70] 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,[71] and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to forming an event horizon.
Once an event horizon forms, Penrose proved that a singularity will form somewhere inside it.[28] Shortly afterwards, Hawking showed that many cosmological solutions describing the Big Bang have singularities without scalar fields or other exotic matter (see Penrose-Hawking singularity theorems). 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.[72] The primary formation process for black holes is expected to be the gravitational collapse of heavy objects such as stars, but there are also more exotic processes that can lead to the production of black holes.
Gravitational collapse
Main article: 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.[73] The collapse may be stopped by the degeneracy pressure of the star's constituents, condensing the matter in an exotic denser state. The result is one of the various types of compact star. The type of compact star formed depends on the mass of the remnant—the matter left over after the outer layers have been blown away, such from a supernova explosion or by pulsations leading to a planetary nebula. Note that this mass can be substantially less than the original star—remnants exceeding 5 solar masses are produced by stars that were over 20 solar masses before the collapse.[73]
If the mass of the remnant exceeds about 3–4 solar masses (the Tolman–Oppenheimer–Volkoff limit[15])—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.[73]
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 103 solar masses. These black holes could be the seeds of the supermassive black holes found in the centers of most galaxies.[74]
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 sees 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.[75]
Primordial black holes in the Big Bang
Gravitational collapse requires great density. In the current epoch of the universe these high densities are only found in stars, but in the early universe shortly after the big bang densities were much greater, possibly allowing for the creation of black holes. The high density alone is not enough to allow the formation of black holes since a uniform mass distribution will not allow the mass to bunch up. In order for primordial black holes to form in such a dense medium, there must be initial density perturbations that can then grow under their own gravity. Different models for the early universe vary widely in their predictions of the size of these perturbations. Various models predict the creation of black holes, ranging from a Planck mass to hundreds of thousands of solar masses.[76] Primordial black holes could thus account for the creation of any type of black hole.
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.[77] 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 (mP = √ħc/G ≈ 1.2×1019 GeV/c2 ≈ 2.2×10−8 kg), where quantum effects are expected to invalidate the predictions of general relativity.[78] 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 Planck mass could be much lower: some braneworldscenarios for example put the boundary as low as 1 TeV/c2.[79] This would make it conceivable for micro black holes to be created in the high-energy collisions occurring when cosmic rays hit the Earth's atmosphere, or possibly in the new Large Hadron Collider at CERN. Yet these theories are very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists.[80] Even if micro black holes should be formed in these collisions, it is expected that they would evaporate in about 10−25 seconds, posing no threat to the Earth.[81]
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 direct surroundings and omnipresent cosmic background radiation. This is the primary process through which supermassive black holes seem to have grown.[74] A similar process has been suggested for the formation of intermediate-mass black holes in globular clusters.[82]
Another possibility is for a black hole to merge with other objects such as stars or even other black holes. Although not necessary for growth, this is thought to have been important, especially for the early development of supermassive black holes, which could have formed from the coagulation of many smaller objects.[74] The process has also been proposed as the origin of some intermediate-mass black holes.[83][84]
Evaporation
Main article: Hawking radiation
In 1974, Hawking showed that black holes are not entirely black but emit small amounts of thermal radiation;[31] an effect that has become known as Hawking radiation. By applyingquantum field theory to a static black hole background, he determined that a black hole should emit particles in a perfect black body spectrum. Since Hawking's publication, many others have verified the result through various approaches.[85] If Hawking's theory of black hole radiation is correct, then black holes are expected to shrink and evaporate over time because they lose mass by the emission of photons and other particles.[31] 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.[86]
A stellar black hole of one solar mass has a Hawking temperature of about 100 nanokelvins. 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 shrink. To have a Hawking temperature larger than 2.7 K (and be able to evaporate), a black hole needs to have less mass than the Moon. Such a black hole would have a diameter of less than a tenth of a millimeter.[87]
If a black hole is very small the radiation effects are expected to become very strong. Even a black hole that is heavy compared to a human would evaporate in an instant. A black hole the weight 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 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/c2 would take less than 10−88 seconds to evaporate completely. For such a small black hole, quantum gravitation effects are expected to play an important role and could even—although current developments in quantum gravity do not indicate so[88]—hypothetically make such a small black hole stable.[89]
Observational evidence
By their very nature, black holes do not directly emit any signals other than the hypothetical Hawking radiation; since the Hawking radiation for an astrophysical black hole is predicted to be very weak, this makes it impossible to directly detect astrophysical black holes from the Earth. A possible exception to the Hawking radiation being weak is the last stage of the evaporation of light (primordial) black holes; searches for such flashes in the past have proven unsuccessful and provide stringent limits on the possibility of existence of light primordial black holes.[91]NASA's Fermi Gamma-ray Space Telescope launched in 2008 will continue the search for these flashes.[92]
Astrophysicists searching for black holes thus have to rely on indirect observations. A black hole's existence can sometimes be inferred by observing its gravitational interactions with its surroundings. A project run by MIT's Haystack Observatory is attempting to observe the event horizon of a black hole directly. Initial results are encouraging.[93]
Accretion of matter
See also: Accretion disc
Due to conservation of angular momentum, gas falling into the gravitational well created by a massive object will typically form a disc-like structure around the object. Friction within the disc causes angular momentum to be transported outward, allowing matter to fall further inward, releasing potential energy and increasing the temperature of the gas.[94] In the case of compact objects such as white dwarfs, neutron stars, and black holes, the gas in the inner regions becomes so hot that it will emit vast amounts of radiation (mainly X-rays), which 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 in radiation.[94] (In nuclear fusion only about 0.7% of the rest mass will be emitted as energy.) In many cases, accretion discs are accompanied by relativistic jets emitted along the poles, which carry away much of the energy. The mechanism for the creation of these jets is currently not well understood.
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 discs of supermassive black holes.[95] 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.[95]It has also been suggested that some ultraluminous X-ray sources may be the accretion disks of intermediate-mass black holes.[96]
X-ray binaries
See also: X-ray binary
X-ray binaries are binary star systems that are luminous in the X-ray part of the spectrum. These X-ray emissions are generally thought to be caused by one of the component stars being a compact object accreting matter from the other (regular) star. The presence of an ordinary star in such a system provides a unique opportunity for studying the central object and determining if it might be a black hole.
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 obtain an estimate for the mass of the compact object. If this is much larger than the Tolman–Oppenheimer–Volkoff limit (that is, the maximum mass a neutron star can have before collapsing) then the object cannot be a neutron star and is generally expected to be a black hole.[95]
The first strong candidate for a black hole, Cygnus X-1, was discovered in this way by Charles Thomas Bolton,[97] Louise Webster and Paul Murdin[98] in 1972.[99][100] Some doubt, however, remained due to the uncertainties resultant from the companion star being much heavier than the candidate black hole.[95] Currently, better candidates for black holes are found in a class of X-ray binaries called soft X-ray transients.[95] In this class of system the companion star is relatively low mass allowing for more accurate estimates in the black hole mass. Moreover, these systems are only active in X-ray for several months once every 10–50 years. During the period of low X-ray emission (called quiescence), the accretion disc is extremely faint allowing for detailed observation of the companion star during this period. One of the best such candidates isV404 Cyg.
Quiescence and advection-dominated accretion flow
The faintness of the accretion disc during quiescence is suspected to be caused by the flow entering a mode called an advection-dominated accretion flow (ADAF). In this mode, almost all the energy generated by friction in the disc is swept along with the flow instead of radiated away. If this model is correct, then it forms strong qualitative evidence for the presence of an event horizon.[101] Because, if the object at the center of the disc had a solid surface, it would emit large amounts of radiation as the highly energetic gas hits the surface, an effect that is observed for neutron stars in a similar state.[94]
Quasi-periodic oscillations
Main article: Quasi-periodic oscillations
The X-ray emission from accretion disks sometimes flickers 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 potential black holes.[102]
Galactic nuclei
See also: Active galactic nucleus
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. 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 gas and dust called an accretion disk; and two jets that are perpendicular to the accretion disk.[103][104]
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, APM08279+5255 and the Sombrero Galaxy.[105]
It is now widely accepted that the center of nearly every galaxy, not just active ones, contains a supermassive black hole.[106] 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 the galaxy itself.[107]
Currently, the best evidence for a supermassive black hole comes from studying the proper motion of stars near the center of our own Milky Way.[109] Since 1995 astronomers have tracked the motion of 90 stars in a region called Sagittarius A*. By fitting their motion to Keplerian orbits they were able to infer in 1998 that 2.6 million solar masses must be contained in a volume with a radius of 0.02 lightyears.[110] Since then one of the stars—called S2—has completed a full orbit. From the orbital data they were able to place better constraints on the mass and size of the object causing the orbital motion of stars in the Sagittarius A* region, finding that there is a spherical mass of 4.3 million solar masses contained within a radius of less than 0.002 lightyears.[109] While this is more than 3000 times the Schwarzschild radius corresponding to that mass, it is at least consistent with the central object being a supermassive black hole, and no "realistic cluster [of stars] is physically tenable".[110]
Effects of strong gravity
Another way that the black hole nature of an object may be tested in the future is through observation of effects caused by strong gravity in their vicinity. One such effect is gravitational lensing: The deformation of spacetime around a massive object causes light rays to be deflected much like 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.[111]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*.[111]
Another option would be the direct observation of gravitational waves produced by an object falling into a black hole, for example a compact object falling into a supermassive black hole through an extreme mass ratio inspiral. Matching the observed waveform to the predictions of general relativity would allow precision measurements of the mass and angular momentum of the central object, while at the same time testing general relativity.[112] These types of events are a primary target for the proposed Laser Interferometer Space Antenna.
Alternatives
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.[95] A phase of free quarks at high density might allow the existence of dense quark stars,[113] and some supersymmetric models predict the existence of Q stars.[114] Some extensions of the standard model posit the existence of preons as fundamental building blocks of quarks andleptons, which could hypothetically form preon stars.[115] These hypothetical models could potentially explain a number of observations of stellar black hole candidates. However, it can be shown from general arguments in general relativity that any such object will have a maximum mass.[95]
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 108 solar mass black hole is comparable to that of water).[95] 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.[95]
The evidence for stellar and supermassive black holes implies that in order for black holes not to form, general relativity must fail as a theory of gravity, perhaps due to the onset ofquantum mechanical corrections. A much anticipated feature of a theory of quantum gravity is that it will not feature singularities or event horizons (and thus no black holes).[116] In recent years[when?], much attention has been drawn by the fuzzball model in string theory. Based on calculations in specific situations in string theory, the proposal suggests that generically the individual states of a black hole solution do not have an event horizon or singularity, but that for a classical/semi-classical observer the statistical average of such states does appear just like an ordinary black hole in general relativity.[117]
Open questions
Entropy and thermodynamics
Further information: Black hole thermodynamics
In 1971, Hawking showed under general conditions[Note 3] that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and merge.[118] 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 a 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 of 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.[119]
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 thefirst law of thermodynamics, with the mass acting as energy, the surface gravity as temperature and the area as entropy.[119]
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.[120]
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 Stromingerand Cumrun Vafa showed that counting the microstates of a specific supersymmetric black hole in string theory reproduced the Bekenstein–Hawking entropy.[121] 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.[122]
Information loss paradox
Main article: Black hole information paradox
| 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. 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.[123]
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 vital property called unitarity, which has to do with the conservation of probability. It has been argued that loss of unitarity would also imply violation of conservation of energy.[124] Over recent years evidence has been building that indeed information and unitarity are preserved in a full quantum gravitational treatment of the problem.[125]
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