Considering the exotic nature of black holes, it may be natural to question if such bizarre objects could actually 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.[44] 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,[45] 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, Roger Penrose proved that a singularity will form somewhere inside it. Shortly afterwards, Stephen Hawking showed that many cosmological solutions describing the big bang have singularities, in the absence of 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.[46] 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
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 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 possibly 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.
Primordial black holes in The Big Bang
Gravitational collapse requires great densities. 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 which 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.[47] 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 also be created in high energy collisions that create sufficient density. However, to date, no such events have ever been detected either directly or indirectly as a deficiency of the mass balance in particle accelerator experiments.[48] 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 (~1019 GeV/c2 = ~2 × 10-8 kg), where quantum effects are expected to make the theory of general relativity break down completely.[citation needed] 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/c2.[49] 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 possibly 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.[citation needed]
Growth
Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb interstellar dust from its direct surroundings and omnipresent cosmic background radiation, but neither of these processes should significantly affect the mass of a stellar black hole. More significant contributions can occur when the black hole formed in a binary star system. After formation the black hole can then leech significant amounts of matter from its companion.
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.
As an object approaches the event horizon, the horizon near the object bulges up and swallows the object. Shortly thereafter the increase in radius (due to the extra mass) is distributed evenly around the hole.
Evaporation
In 1974, Stephen Hawking showed that black holes are not entirely black but emit small amounts of thermal radiation.[50] He got this result by applying quantum field theory in a static black hole background. The result of his calculations is that a black hole should emit particles in a perfect black body spectrum. This effect has become known as Hawking radiation. Since Hawking's result, many others have verified the effect through various methods.[51] If his theory of black hole radiation is correct then black holes are expected to emit a thermal spectrum of radiation, and thereby lose mass, because according to the theory of relativity mass is just highly condensed energy (E = mc2).[50] Black holes will shrink and evaporate over time. The temperature of this 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. Large black holes, therefore, emit less radiation than small black holes.
A stellar black hole of 5 solar masses has a Hawking temperature of about 12 nanokelvins. This is far less than the 2.7 K produced by the cosmic microwave background. Stellar mass (and larger) black holes receive more mass from the cosmic microwave background 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 be able to evaporate) a black hole needs to be lighter than the Moon (and therefore a 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.
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 holes 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 has proven unsuccessful and provides stringent limits on the possibility of existence of light primordial black holes.[52] NASA's Fermi Gamma-ray Space Telescope launched in 2008 will continue the search for these flashes.[53]
Astrophysicists searching for black holes thus have to rely on indirect observations. Using the gravitational interactions between a black hole and its surrounding its it is sometimes possible to infer its existence.
Accretion of matter
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.[54] 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 process known; up to 40% of the rest mass of the accreted material can be emitted in radiation.[54] (In nuclear fusion only about 1% of the rest mass will be emitted as energy.) In many cases accretion discs are accompanied by relativistic jets emitted along the poles, carry away a lot 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 thought to be the accretion discs of supermassive black holes.[citation needed] Similarly, X-ray binaries are thought to be binary star systems in which one of the two stars is a compact object accreting matter from its companion.[citation needed] It has also been suggested that some ultraluminous X-ray sources may be the accretion disks of intermediate-mass black holes.[55]
X-ray binaries
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 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 (ie. 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.[56]
The first strong candidate for a black hole, Cygnus X-1, was discovered in this way by Webster and Murdin[57] and Bolton[58] in 1972.[59][60] Some doubt however remained due to the uncertainties resultant from the companion star being much heavier than the candidate black hole.[56] Currently, better candidates for black holes are found in a class of X-ray binaries called soft X-ray transients.[56] In this class of system the companion star is relatively low mass allowing for more accurate estimates in the black hole mass. Moreover, these system are only active in X-ray for a period of several months once every 10-50 years. During the period of low X-ray emission (called quiescence) the accretion disc is extemely faint allowing for detailed observation of the companion star during this period. One of the best such candidates is V404 Cyg.
Quiescence and advection-dominated accretion flow
The faintness of the accretion disc during quiescence is thought 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. Because, if the object at the center of the disc had a solid surface, it would emit large amounts of radiation is the highly energetic gas hits the surface, an effect that is observed for neutron stars in a similar state.[54]
Quasi-periodic oscillations
The X-ray emissions from accretion disks sometimes exhibit a flickering around 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.[61]
Gamma ray bursts
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[62] or by collisions between neutron stars,[63] 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,[64] 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[65] so the black holes associated with them are actually billions of years old.
Gravitational lensing
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.
Galactic Nuclei
It is now widely accepted that the center of every or at least nearly every galaxy contains a supermassive black hole.[66][67] 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.[66]
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.[68][69] However, theoretical and observational studies have shown that the active galactic nuclei (AGN) in these galaxies may contain supermassive black holes.[68][69] 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.[69]
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.[70]
Currently, the best evidence for a supermassive black hole comes from the center of our own Milky way.[71] For sixteen years astronomers have tracked the positions of stars orbiting a central massive object in a region called Sagittarius A*, one of which—as star called S2— has completed a full orbit in that period. From the orbital data they were able to infer that there was a spherical mass of 4.3 million solar masses contained within a radius of less than 0.002 lightyears. This is still more than 3000 times the Schwarzschild radius corresponding to that mass. This is consistent with the central object being a supermassive black hole.
Open questions
Entropy and Hawking radiation
In 1971, Stephen Hawking showed that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and swallow each other; that is merge.[72] This is remarkably similar to the Second Law of Thermodynamics, with area playing the role of entropy. As a classical object with 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 the black hole, resulting in a decrease of the total entropy of the universe. Therefore, Jacob Bekenstein proposed that a black hole should have an entropy, and that it should be proportional to its horizon area. Since black holes do not classically emit radiation, the thermodynamic viewpoint seemed simply an analogy, since zero temperature implies infinite changes in entropy with any addition of heat, which implies infinite entropy. However, in 1974, Hawking applied quantum field theory to the curved spacetime around the event horizon and discovered that black holes emit Hawking radiation, a form of thermal radiation, allied to the Unruh effect, which implied they had a positive temperature. This strengthened the analogy being drawn between black hole dynamics and thermodynamics: using the first law of black hole mechanics, it follows that the entropy of a non-rotating black hole is one quarter of the area of the horizon. This is a universal result and can be extended to apply to cosmological horizons such as in de Sitter space. It was later suggested that black holes are maximum-entropy objects, meaning that the maximum possible entropy of a region of space is the entropy of the largest black hole that can fit into it. This led to the holographic principle.
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, which 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 hole unitarity
An open question in fundamental physics is the so-called information loss paradox, or black hole unitarity paradox. Classically, the laws of physics are the same run forward or in reverse (T-symmetry). Liouville's Theorem dictates conservation of phase space volume, which can be thought of as 'conservation of information', so there is some problem even in classical (non-quantum general relativity) physics. In quantum mechanics, this corresponds to a vital property called unitarity, which has to do with the conservation of probability (It can also be thought of as a conservation of quantum phase space volume as expressed by the density matrix).[73]
Fuzzballs
Fuzzballs are theorized by some superstring theory scientists to be the true quantum description of black holes. The theory resolves the information paradox eliminates the need for a singularity at the heart of the black hole with infinite spacetime curvature due to an infinitely intense gravitational field from a region of zero volume. Modern physics breaks down when such parameters are infinite and zero.
Samir Mathur of Ohio State University, with postdoctoral researcher Oleg Lunin, proposed via two papers in 2002 that black holes are actually spheres of strings with a definite volume; they are not a singularity, which the classic view holds to be a zero-dimensional, zero-volume point into which a black hole’s entire mass is concentrated.[74]
String theory holds that the fundamental constituents of subatomic particles, including the force carriers (e.g., quarks leptons, photons, and gluons), all comprise a one-dimensional string of energy that takes on its identity by vibrating in different modes and/or frequencies. Quite unlike the view of a black hole as a singularity, a small fuzzball can be thought of as an extra-dense neutron star where its neutrons have decomposed, or “melted,” liberating the quarks (strings in string theory) comprising them. Accordingly, fuzzballs can be regarded as the most extreme form of degenerate matter.
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