Cosmic body with gravity (see gravitation) so intense that nothing, not even light, can escape. It is suspected to form in the death and collapse of a star that has retained at least three times the Sun's mass. Stars with less mass evolve into white dwarf stars or neutron stars. Details of a black hole's structure are calculated from Albert Einstein's general theory of relativity: a “singularity” of zero volume and infinite density pulls in all matter and energy that comes within an event horizon, defined by the Schwarzschild radius, around it. Black holes cannot be observed directly because they are small and emit no light. However, their enormous gravitational fields affect nearby matter, which is drawn in and emits X rays as it collides at high speed outside the event horizon. Some black holes may have nonstellar origins. Astronomers speculate that supermassive black holes at the centres of quasars and many galaxies are the source of energetic activity that is observed. Stephen W. Hawking theorized the creation of numerous tiny black holes, possibly no more massive than an asteroid, during the big bang. These primordial “mini black holes” lose mass over time and disappear as a result of Hawking radiation. Although black holes remain theoretical, the case for their existence is supported by many observations of phenomena that match their predicted effects.
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A black hole is a theoretical region of space in which the gravitational field is so powerful that nothing, not even electromagnetic radiation (e.g. visible light), can escape its pull after having fallen past its event horizon. The term derives from the fact that the absorption of visible light renders the hole's interior invisible, and indistinguishable from the black space around it.
Despite its interior being invisible, a black hole may reveal its presence through an interaction with matter that lies in orbit outside its event horizon. For example, a black hole may be perceived by tracking the movement of a group of stars that orbit its center. Alternatively, one may observe gas (from a nearby star, for instance) that has been drawn into the black hole. The gas spirals inward, heating up to very high temperatures and emitting large amounts of radiation that can be detected from earthbound and earth-orbiting telescopes. Such observations have resulted in the general scientific consensus that—barring a breakdown in our understanding of nature—black holes do exist in our universe.
The idea of an object with gravity strong enough to prevent light from escaping was proposed in 1783 by John Michell, an amateur British astronomer. In 1795, Pierre-Simon Laplace, a French physicist independently came to the same conclusion. Black holes, as currently understood, are described by the general theory of relativity. This theory predicts that when a large enough amount of mass is present in a sufficiently small region of space, all paths through space are warped inwards towards the center of the volume, preventing all matter and radiation within it from escaping.
While general relativity describes a black hole as a region of empty space with a point-like singularity at the center and an event horizon at the outer edge, the description changes when the effects of quantum mechanics are taken into account. Research on this subject indicates that, rather than holding captured matter forever, black holes may slowly leak a form of thermal energy called Hawking radiation and may well have a finite life. However, the final, correct description of black holes, requiring a theory of quantum gravity, is unknown.
Simulated view of a black hole in front of the Milky Way. The hole has 10 solar masses and is viewed from a distance of 600 km.
According to Einstein’s general theory of relativity, as mass is added to a degenerate star a sudden collapse will take place and the intense gravitational field of the star will close in on itself. Such a star then forms a "black hole" in the universe.
The phrase had already entered the language years earlier as the Black Hole of Calcutta incident of 1756 in which 146 Europeans were locked up overnight in punishment cell of barracks at Fort William by Siraj ud-Daulah, and all but 23 perished.
Far away from the black hole a particle can move in any direction. 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.
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.
Two concepts introduced by Albert Einstein are needed to explain the phenomenon. The first is that time and space are not two independent concepts, but are interrelated forming a single continuum, spacetime. This continuum has some special properties. An object is not free to move around spacetime at will; it must always move forward in time and cannot change its position in space faster than the speed of light. This is the main result of the theory of special relativity.
The second concept is the base of general relativity; mass deforms the structure of this spacetime. The effect of a mass on spacetime can informally be described as tilting the direction of time towards the mass. As a result, objects tend to move towards masses. This is experienced as gravity. This tilting effect becomes more pronounced as the distance to the mass becomes smaller. At some point close to the mass, the tilting becomes so strong that all the possible paths an object can take lead towards the mass. This implies that any object that crosses this point can no longer get further away from the mass, not even using powered flight. This point is called the event horizon.
The "No Hair" theorem does make some assumptions about the nature of our universe and the matter it contains. Other assumptions would lead to different conclusions. For example, if nature allows magnetic monopoles to exist—which appears to be theoretically possible, but has never been observed—then it should also be possible for a black hole to have a magnetic charge. If the universe has more than four dimensions (as string theories, a controversial but apparently possible class of theories, would require), or has a global anti-de Sitter structure, the theorem could fail completely, allowing many sorts of "hair". However, in our apparently four-dimensional, very nearly flat universe, the theorem should hold.
More general black hole solutions were discovered later in the 20th century. The Reissner-Nordström solution describes a black hole with electric charge, while the Kerr solution yields a rotating black hole. The most general known stationary black hole solution is the Kerr-Newman metric having both charge and angular momentum. All these general solutions share the property that they converge to the Schwarzschild solution at distances that are large compared to the ratio of charge and angular momentum to mass (in natural units).
While the mass of a black hole can take any (positive) value, the other two properties, charge and angular momentum, are constrained by the mass. In natural units , the total charge Q and the total angular momentum J are expected to satisfy Q2+(J/M)2 ≤ M2 for a black hole of mass M. Black holes saturating this inequality are called extremal. Solutions of Einstein's equation violating the inequality do exist, but do not have a horizon. These solutions have naked singularities and are thus deemed unphysical. The cosmic censorship hypothesis states that it is impossible for such singularities to form in due to gravitational collapse of generic realistic matter. This is supported by numerical simulations.
Black holes forming from the collapse of stars are expected—due to the relatively large strength of electromagnetic force—to retain the nearly neutral charge of the star. Rotation, however, is expected to be a common feature of compact objects, and the black-hole candidate binary X-ray source GRS 1915+105 appears to have an angular momentum near the maximum allowed value.
|Supermassive black hole||~105 - 109 MSun||~0.001 - 10 AU|
|Intermediate-mass black hole||~103 MSun||~103 km = REarth|
|Stellar-mass black holes||~10 MSun||~30 km|
|Primordial black hole||up to ~MMoon||up to ~0.1 mm|
Outside of the event horizon, the gravitational field is identical to the field produced by any other spherically symmetric object of the same mass. The popular conception of black holes as "sucking" things in is false: objects can maintain an orbit around black holes indefinitely, provided they stay outside the photon sphere (described below), and also ignoring the effects of gravitational radiation, which causes orbiting objects to lose energy, similar to the effect of electromagnetic radiation.
The singularity in a non-rotating black hole is a point, in other words it has zero length, width, and height. The singularity of a rotating black hole is smeared out to form a ring shape lying in the plane of rotation. The ring still has no thickness and hence no volume.
The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. This breakdown is not unexpected, as it occurs in a situation where quantum mechanical effects should become important, since densities are high and particle interactions should thus play a role. Unfortunately, to date it has not been possible to combine quantum and gravitation effects in a single theory. It is however quite generally expected that a theory of quantum gravity will feature black holes without singularities.
Note, however, that formation of the singularity takes finite (and very short) time only from the point of view of an observer which resides in collapsing object. From the point of view of distant observer, it takes infinite time to do so due to gravitational time dilation.
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.
Other compact objects, such as neutron stars, can also have photon spheres. This follows from the fact gravitation 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 in fact have a photon sphere.
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.
The ergosphere of black hole is bounded by
Within the ergosphere, space-time is dragged around faster than light—general relativity forbids material objects to travel faster than light (so does special relativity), but allows regions of space-time to move faster than light relative to other regions of space-time.
Objects and radiation (including light) can stay in orbit within the ergosphere without falling to the center. But they cannot hover (remain stationary, as seen by an external observer), because that would require them to move backwards faster than light relative to their own regions of space-time, which are moving faster than light relative to an external observer.
Objects and radiation can also escape from the ergosphere. In fact the Penrose process predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way, the black hole will spin more slowly and may even stop spinning eventually.
The temperature of the emitted black body spectrum is proportional to the surface gravity of the black hole. For a Schwarzschild black hole this is inversely proportional to the mass. Consequently, large black holes are very cold and emit very little radiation. A stellar black hole of 10 solar masses, for example, would have a Hawking temperature of several nanokelvin, much less than the 2.7K produced by the Cosmic Microwave Background. Micro black holes on the other hand could be quite bright producing high energy gamma rays.
Due to low Hawking temperature of stellar black holes, Hawking radiation has never been observed at any of the black hole candidates.
The strength of the tidal force of a black hole depends on how gravitational attraction changes with distance, rather than on the absolute force being felt. This means that small black holes cause spaghettification while infalling objects are still outside their event horizons, whereas objects falling into large, supermassive black holes may not be deformed or otherwise feel excessively large forces before passing the event horizon.
From the viewpoint of a distant observer, an object falling into a black hole appears to slow down, approaching but never quite reaching the event horizon: and it appears to become redder and dimmer, because of the extreme gravitational red shift caused by the gravity of the black hole. Eventually, the falling object becomes so dim that it can no longer be seen, at a point just before it reaches the event horizon. All of this is a consequence of time dilation: the object's movement is one of the processes that appear to run slower and slower, and the time dilation effect is more significant than the acceleration due to gravity; the frequency of light from the object appears to decrease, making it look redder, because the light appears to complete fewer cycles per "tick" of the observer's clock; lower-frequency light has less energy and therefore appears dimmer, as well as redder.
From the viewpoint of the falling object, distant objects generally appear blue-shifted due to the gravitational field of the black hole. This effect may be partly (or even entirely) negated by the red shift caused by the velocity of the infalling object with respect to the object in the distance.
The amount of proper time a faller experiences below the event horizon depends upon where they started from rest, with the maximum being for someone who starts from rest at the event horizon. A paper in 2007 examined the effect of firing a rocket pack within the black hole, showing that this can only reduce the proper time of a person who starts from rest at the event horizon. However, for anyone else, a judicious burst of the rocket can extend the lifetime of the faller, but overdoing it will again reduce the proper time experienced. However, this cannot prevent the inevitable collision with the central singularity.
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, or because a star which would have been stable receives a lot of extra matter in a way which 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 (the ideal gas law explains the connection between pressure, temperature, and volume).
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. Which type of compact star is formed depends on the mass of the remnant - the matter left over after changes triggered by the collapse (such as supernova or pulsations leading to a planetary nebula) have blown away the outer layers. Note that this can be substantially less than the original star - remnants exceeding 5 solar masses are produced by stars which were over 20 solar masses before the collapse.
If the mass of the remnant of exceeds ~3-4 solar masses (the Tolman-Oppenheimer-Volkoff limit)—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. After this no known mechanism (except maybe the quark degeneracy pressure, see quark star) is powerful enough to stop the collapse and the object will inevitably collapse to a black hole.
This gravitational collapse of heavy stars is assumed to be responsible for the formation of most (if not all) stellar mass black holes.
Theoretically this bound is expect to lie around the Planck mass (~1019 GeV/c2), where quantum effects are expected to make the theory of general relativity break down completely. This would put the creation of black holes firmly out of reach of any high energy process occurring on or near the Earth. Certain developments in quantum gravity however suggest that this bound could be much lower. Some braneworld scenarios for example put the Planck mass much lower, may be even as low as 1 TeV. This would make it possible for micro black holes to be created in the high energy collisions occurring when cosmic rays hit the earth's atmosphere, or even maybe in the new Large Hadron Collider at CERN. These theories are however very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists.
Much larger contributions can be obtained when a black hole merges with other stars or compact objects. The supermassive black holes suspected in the center of most galaxies are expected to have formed from the coagulation of many smaller objects. The process has also been proposed as the origin of some intermediate-mass black holes.
A stellar black hole of 5 solar masses has a Hawking temperature of about 12 nanoKelvin. This is far less than the 2.7 K produced by the Cosmic microwave background. Stellar mass (and larger) black holes thus receive more mass from the CMB than they emit through Hawking radiation and will thus grow instead of shrink. In order to have a Hawking temperature larger than 2.7 K (and thus be able to evaporate) a black hole needs to be lighter than the Moon (and thus have diameter of less than a tenth of a millimeter).
On the other hand 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 (~ 10-24 m) would only take a nanosecond to evaporate, during which time it would briefly have a luminosity more than 200 times that of the sun. Lighter 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. Of course, 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— hypothetically make such a small black hole stable.
Most accretion disks and gas jets are not clear proof that a stellar-mass black hole is present, because other massive, ultra-dense objects such as neutron stars and white dwarfs cause accretion disks and gas jets to form and to behave in the same ways as those around black holes. But they can often help by telling astronomers where it might be worth looking for a black hole.
On the other hand, extremely large accretion disks and gas jets may be good evidence for the presence of supermassive black holes, because as far as we know any mass large enough to power these phenomena must be a black hole.
Steady X-ray and gamma ray emissions also do not prove that a black hole is present, but can tell astronomers where it might be worth looking for one - and they have the advantage that they pass fairly easily through nebulae and gas clouds.
But strong, irregular emissions of X-rays, gamma rays and other electromagnetic radiation can help to prove that a massive, ultra-dense object is not a black hole, so that "black hole hunters" can move on to some other object. Neutron stars and other very dense stars have surfaces, and matter colliding with the surface at a high percentage of the speed of light will produce intense flares of radiation at irregular intervals. Black holes have no material surface, so the absence of irregular flares around a massive, ultra-dense object suggests that there is a good chance of finding a black hole there.
Intense but one-time gamma ray bursts (GRBs) may signal the birth of "new" black holes, because astrophysicists think that GRBs are caused either by the gravitational collapse of giant stars or by collisions between neutron stars, and both types of event involve sufficient mass and pressure to produce black holes. But it appears that a collision between a neutron star and a black hole can also cause a GRB, so a GRB is not proof that a "new" black hole has been formed. All known GRBs come from outside our own galaxy, and most come from billions of light years away so the black holes associated with them are actually billions of years old.
Quasars are thought to be the accretion disks of supermassive black holes, since no other known object is powerful enough to produce such strong emissions. Quasars produce strong emission across the electromagnetic spectrum, including UV, X-rays and gamma-rays and are visible at tremendous distances due to their high luminosity. Between 5 and 25% of quasars are "radio loud," so called because of their powerful radio emission.
A gravitational lens is formed when the light from a very distant, bright source (such as a quasar) is "bent" around a massive object (such as a black hole) between the source object and the observer. The process is known as gravitational lensing, and is one of the predictions of the general theory of relativity. According to this theory, mass "warps" space-time to create gravitational fields and therefore bend light as a result.
A source image behind the lens may appear as multiple images to the observer. In cases where the source, massive lensing object, and the observer lie in a straight line, the source will appear as a ring behind the massive object.
Gravitational lensing can be caused by objects other than black holes, because any very strong gravitational field will bend light rays. Some of these multiple-image effects are probably produced by distant galaxies.
Unfortunately, since the time of Johannes Kepler, astronomers have had to deal with the complications of real astronomy:
According to the American Astronomical Society, every large galaxy has a supermassive black hole at its center. The black hole’s mass is proportional to the mass of the host galaxy, suggesting that the two are linked very closely. The Hubble Space Telescope and ground-based telescopes in Hawaii were used in a large survey of galaxies.
For decades, astronomers have used the term "active galaxy" to describe galaxies with unusual characteristics, such as unusual spectral line emission and very strong radio emission. However, theoretical and observational studies have shown that the active galactic nuclei (AGN) in these galaxies may contain 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.
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, and the Sombrero Galaxy.
In November 2004 a team of astronomers reported the discovery of the first well-confirmed intermediate-mass black hole in our Galaxy, orbiting three light-years from Sagittarius A*. This black hole of 1,300 solar masses is within a cluster of seven stars, possibly the remnant of a massive star cluster that has been stripped down by the Galactic Centre. This observation may add support to the idea that supermassive black holes grow by absorbing nearby smaller black holes and stars.
In January 2007, researchers at the University of Southampton in the United Kingdom reported finding a black hole, possibly of about 10 solar masses, in a globular cluster associated with a galaxy named NGC 4472, some 55 million light-years away.
Our Milky Way galaxy contains several probable stellar-mass black holes which are closer to us than the supermassive black hole in the Sagittarius A* region. These candidates are all members of X-ray binary systems in which the denser object draws matter from its partner via an accretion disk. The probable black holes in these pairs range from three to more than a dozen solar masses. The most distant stellar-mass black hole ever observed is a member of a binary system located in the Messier 33 galaxy.
In theory there is no smallest size for a black hole. Once created, it has the properties of a black hole. Stephen Hawking theorized that primordial black holes could evaporate and become even tinier, i.e. micro black holes. Searches for evaporating primordial black holes are proposed for the GLAST satellite to be launched in 2008. However, if micro black holes can be created by other means, such as by cosmic ray impacts or in colliders, that does not imply that they must evaporate.
The formation of black hole analogs on Earth in particle accelerators has been reported. These black hole analogs are not the same as gravitational black holes, but they are vital testing grounds for quantum theories of gravity.
They act like black holes because of the correspondence between the theory of the strong nuclear force, which has nothing to do with gravity, and the quantum theory of gravity. They are similar because both are described by string theory. So the formation and disintegration of a fireball in quark gluon plasma can be interpreted in black hole language. The fireball at the Relativistic Heavy Ion Collider [RHIC] is a phenomenon which is closely analogous to a black hole, and many of its physical properties can be correctly predicted using this analogy. The fireball, however, is not a gravitational object. It is presently unknown whether the much more energetic Large Hadron Collider [LHC] would be capable of producing the speculative large extra dimension micro black hole, as many theorists have suggested.
If the semi-diameter of a sphere of the same density as the Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to its vis inertiae, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity.
This assumes that light is influenced by gravity in the same way as massive objects.
In 1796, the mathematician Pierre-Simon Laplace promoted the same idea in the first and second editions of his book Exposition du système du Monde (it was removed from later editions).
The idea of black holes was largely ignored in the nineteenth century, since light was then thought to be a massless wave and therefore not influenced by gravity. Unlike a modern black hole, the object behind the horizon is assumed to be stable against collapse.
In 1930, the astrophysicist Subrahmanyan Chandrasekhar argued that, according to special relativity, a non-rotating body above 1.44 solar masses (the Chandrasekhar limit), would collapse since there was nothing known at that time could stop it from doing so. His arguments were opposed by Arthur Eddington, who believed that something would inevitably stop the collapse. Eddington was partly right: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star. But in 1939, Robert Oppenheimer published papers (with various co-authors) which predicted that stars above about three solar masses (the Tolman-Oppenheimer-Volkoff limit) would collapse into black holes for the reasons presented by Chandrasekhar.
Oppenheimer and his co-authors used Schwarzschild's system of coordinates (the only coordinates available in 1939), which produced mathematical singularities at the Schwarzschild radius, in other words the equations broke down at the Schwarzschild radius because some of the terms were infinite. This was interpreted as indicating that the Schwarzschild radius was the boundary of a "bubble" in which time "stopped". For a few years the collapsed stars were known as "frozen stars" because the calculations indicated that an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius. But many physicists could not accept the idea of time standing still inside the Schwarzschild radius, and there was little interest in the subject for over 20 years.
In 1958 David Finkelstein broke the deadlock over "stopped time" and introduced the concept of the event horizon by presenting the Eddington-Finkelstein coordinates, which enabled him to show that "The Schwarzschild surface r = 2 m is not a singularity but acts as a perfect unidirectional membrane: causal influences can cross it but only in one direction". Note that at this stage all theories, including Finkelstein's, covered only non-rotating, uncharged black holes.
In 1963 Roy Kerr extended Finkelstein's analysis by presenting the Kerr metric (coordinates) and showing how this made it possible to predict the properties of rotating black holes. In addition to its theoretical interest, Kerr's work made black holes more believable for astronomers, since black holes are formed from stars and all known stars rotate.
In 1967 astronomers discovered pulsars, and within a few years could show that the known pulsars were rapidly rotating neutron stars. Until that time, neutron stars were also regarded as just theoretical curiosities. So the discovery of pulsars awakened interest in all types of ultra-dense objects that might be formed by gravitational collapse.
In 1970, Stephen Hawking and Roger Penrose proved that black holes are a feature of all solutions to Einstein's equations of gravity, not just of Schwarzschild's, and therefore black holes cannot be avoided in some collapsing objects.
In 1971, Louise Webster and Paul Murdin, at the Royal Greenwich Observatory, and Charles Thomas Bolton, working independently at the University of Toronto's David Dunlap Observatory, observed HDE 226868 wobble, as if orbiting around an invisible but massive companion. Further analysis led to the declaration that the companion, Cygnus X-1, was in fact a black hole.
In March 2005, physicist George Chapline at the Lawrence Livermore National Laboratory in California proposed that black holes do not exist, and that objects currently thought to be black holes are actually dark-energy stars. He draws this conclusion from some quantum mechanical analyses. Although his proposal currently has little support in the physics community, it was widely reported by the media. A similar theory about the non-existence of black holes was later developed by a group of physicists at Case Western Reserve University in June 2007.
Among the alternate models are magnetospheric eternally collapsing objects, clusters of elementary particles (e.g., boson stars), fermion balls, self-gravitating, degenerate heavy neutrinos and even clusters of very low mass (~0.04 solar mass) black holes.
The Hawking radiation reflects a characteristic temperature of the black hole, which can be calculated from its entropy. The more its temperature falls, the more massive a black hole becomes: the more energy a black hole absorbs, the colder it gets. A black hole with roughly the mass of the planet Mercury would have a temperature in equilibrium with the cosmic microwave background radiation (about 2.73 K). More massive than this, a black hole will be colder than the background radiation, and it will gain energy from the background faster than it gives energy up through Hawking radiation, becoming even colder still. However, for a less massive black hole the effect implies that the mass of the black hole will slowly evaporate with time, with the black hole becoming hotter and hotter as it does so. Although these effects are negligible for black holes massive enough to have been formed astronomically, they would rapidly become significant for hypothetical smaller black holes, where quantum-mechanical effects dominate. Indeed, small black holes are predicted to undergo runaway evaporation and eventually vanish in a burst of radiation.
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 which have the same macroscopic qualities(such as mass, charge, pressure, etc.). But without a satisfactory theory of quantum gravity, one cannot perform such a computation for black holes. Some promise has been shown by string theory, however. There one posits that the microscopic degrees of freedom of the black hole are D-branes. By counting the states of D-branes with given charges and energy, the entropy for certain supersymmetric black holes has been reproduced. Extending the region of validity of these calculations is an ongoing area of research.
Black holes, however, might violate this rule. The position under classical general relativity is subtle but straightforward: because of the classical no hair theorem, we can never determine what went into the black hole. However, as seen from the outside, information is never actually destroyed, as matter falling into the black hole takes an infinite time to reach the event horizon.
Ideas about quantum gravity, on the other hand, suggest that there can only be a limited finite entropy (i.e. a maximum finite amount of information) associated with the space near the horizon; but the change in the entropy of the horizon plus the entropy of the Hawking radiation is always sufficient to take up all of the entropy of matter and energy falling into the black hole.
Many physicists are concerned however that this is still not sufficiently well understood. In particular, at a quantum level, is the quantum state of the Hawking radiation uniquely determined by the history of what has fallen into the black hole; and is the history of what has fallen into the black hole uniquely determined by the quantum state of the black hole and the radiation? This is what determinism, and unitarity, would require.
For a long time Stephen Hawking had opposed such ideas, holding to his original 1975 position that the Hawking radiation is entirely thermal and therefore entirely random, containing none of the information held in material the hole has swallowed in the past; this information he reasoned had been lost. However, on 21 July 2004 he presented a new argument, reversing his previous position. On this new calculation, the entropy (and hence information) associated with the black hole escapes in the Hawking radiation itself. However, making sense of it, even in principle, is difficult until the black hole completes its evaporation. Until then it is impossible to relate in a 1:1 way the information in the Hawking radiation (embodied in its detailed internal correlations) to the initial state of the system. Once the black hole evaporates completely, such identification can be made, and unitarity is preserved.
By the time Hawking completed his calculation, it was already very clear from the AdS/CFT correspondence that black holes decay in a unitary way. This is because the fireballs in gauge theories, which are analogous to Hawking radiation, are unquestionably unitary. Hawking's new calculation has not been evaluated by the specialist scientific community, because the methods he uses are unfamiliar and of dubious consistency; but Hawking himself found it sufficiently convincing to pay out on a bet he had made in 1997 with Caltech physicist John Preskill, to considerable media interest.