A black hole is a region of spacetime from which nothing, not even light, can escape.[1] The theory of general relativity predicts that a sufficiently compact masswill deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that marks the point of no return. It is called "black" because it absorbs all the light that hits the horizon, reflecting nothing, just like a perfect black body in thermodynamics.[2] Quantum mechanics predicts that black holes emit radiation like a black body with a finitetemperature. This temperature is inversely proportional to the mass of the black hole, making it difficult to observe this radiation for black holes of stellar mass or greater.
Objects whose gravity field is too strong for light to escape were first considered in the 18th century by John Michell and Pierre-Simon Laplace. The first modern solution of general relativity that would characterize a black hole was found by Karl Schwarzschild in 1916, although its interpretation as a region of space from which nothing can escape was not fully appreciated for another four decades. Long considered a mathematical curiosity, it was during the 1960s that theoretical work showed black holes were a generic prediction of general relativity. The discovery ofneutron stars sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality.
Black holes of stellar mass are expected to form when massive stars collapse in asupernova at the end of their life cycle. After a black hole has formed it can continue to grow by absorbing mass from its surroundings. By absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses may be formed.
Despite its invisible interior, the presence of a black hole can be inferred through its interaction with other matter. Astronomers have identified numerous stellar black hole candidates in binary systems, by studying their interaction with their companion stars. There is growing consensus that supermassive black holes exist in the centers of most galaxies. In particular, there is strong evidence of a black hole of more than 4 million solar masses at the center of our Milky Way.
| General relativity |
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| Introduction Mathematical formulation Resources |
History
The idea of a body so massive that even light could not escape was first put forward bygeologist John Michell in a letter written to Henry Cavendish in 1783 of the Royal Society:
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.—John Michell[3]
In 1796, 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).[4][5]Such "dark stars" were largely ignored in the nineteenth century, since it was not understood how a massless wave such as light could be influenced by gravity.[6]
General relativity
In 1915, Albert Einstein developed his theory of general relativity, having earlier shown that gravity does influence light's motion. Only a few months later, Karl Schwarzschild found a solution to Einstein field equations, which describes the gravitational field of a point mass and a spherical mass.[7] A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass and wrote more extensively about its properties.[8] This solution had a peculiar behaviour at what is now called theSchwarzschild radius, where it became singular, meaning that some of the terms in the Einstein equations became infinite. The nature of this surface was not quite understood at the time. In 1924, Arthur Eddington showed that the singularity disappeared after a change of coordinates (see Eddington–Finkelstein coordinates), although it took until 1933 for Georges Lemaître to realize that this meant the singularity at the Schwarzschild radius was an unphysical coordinate singularity.[9]
In 1931, Subrahmanyan Chandrasekhar calculated, using general relativity, that a non-rotating body of electron-degenerate matter above a certain limiting mass (now called the Chandrasekhar limit at 1.4 solar masses) must have an infinite density. In other words, the object must have a radius of zero.[10] His arguments were opposed by many of his contemporaries like Eddington and Lev Landau, who argued that some yet unknown mechanism would stop the collapse.[11] They were partly correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star,[12] which is itself stable because of the Pauli exclusion principle. But in 1939, Robert Oppenheimer and others predicted that neutron stars above approximately three solar masses (the Tolman–Oppenheimer–Volkoff limit) would collapse into black holes for the reasons presented by Chandrasekhar, and concluded that no law of physics was likely to intervene and stop at least some stars from collapsing to black holes.[13]
Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infalling observers. Because of this property, the collapsed stars were called "frozen stars,"[14] because 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.
Golden age
See also: Golden age of general relativity
In 1958, David Finkelstein identified the Schwarzschild surface as an event horizon, "a perfect unidirectional membrane: causal influences can cross it in only one direction".[15] This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. Finkelstein's solution extended the Schwarzschild solution for the future of observers falling into a black hole. A complete extension had already been found by Martin Kruskal, who was urged to publish it.[16]
These results came at the beginning of the golden age of general relativity, which was marked by general relativity and black holes becoming mainstream subjects of research. This process was helped by the discovery of pulsars in 1967,[17][18] which were shown to be rapidly rotatingneutron stars by 1969.[19] Until that time, neutron stars, like black holes, were regarded as just theoretical curiosities; but the discovery of pulsars showed their physical relevance and spurred a further interest in all types of compact objects that might be formed by gravitational collapse.
In this period more general black hole solutions were found. In 1963, Roy Kerr found the exact solution for a rotating black hole. Two years later, Ezra Newman found the axisymmetric solution for a black hole that is both rotating and electrically charged.[20] Through the work ofWerner Israel,[21] Brandon Carter,[22][23] and David Robinson[24] the no-hair theorem emerged, stating that a stationary black hole solution is completely described by the three parameters of the Kerr–Newman metric; mass, angular momentum, and electric charge.[25]
For a long time,[vague] it was suspected that the strange features of the black hole solutions were pathological artifacts from the symmetry conditions imposed, and that the singularities would not appear in generic situations. This view was held in particular by Vladimir Belinsky,Isaak Khalatnikov, and Evgeny Lifshitz, who tried to prove that no singularities appear in generic solutions. However, in the late sixties Roger Penrose[26] and Stephen Hawking used global techniques to prove that singularities are generic.[27]
Work by James Bardeen, Jacob Bekenstein, Carter, and Hawking in the early 1970s led to the formulation of black hole thermodynamics.[28]These laws describe the behaviour of a black hole in close analogy to the laws of thermodynamics by relating mass to energy, area toentropy, and surface gravity to temperature. The analogy was completed when Hawking, in 1974, showed that quantum field theory predicts that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole.[29]
The term "black hole" was first publicly used by John Wheeler during a lecture in 1967. Although he is usually credited with coining the phrase, he always insisted that it was suggested to him by somebody else. The first recorded use of the term is in a 1964 letter by Anne Ewing to the American Association for the Advancement of Science.[30] After Wheeler's use of the term, it was quickly adopted in general use.
Properties and structure
The no-hair theorem states that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, charge, and angular momentum.[25] Any two black holes that share the same values for these properties, or parameters, are indistinguishable according to classical (i.e. non-quantum) mechanics.
These properties are special because they are visible from outside a black hole. For example, a charged black hole repels other like charges just like any other charged object. Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law, the ADM mass, far away from the black hole.[31] Likewise, the angular momentum can be measured from far away using frame dragging by the gravitomagnetic field.
When an object falls into a black hole, any information about the shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers. The behavior of the horizon in this situation is a dissipative system that is closely analogous to that of a conductive stretchy membrane with friction and electrical resistance—the membrane paradigm.[32] This is different from other field theories like electromagnetism, which do not have any friction or resistivity at the microscopic level, because they aretime-reversible. Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in. The information that is lost includes every quantity that cannot be measured far away from the black hole horizon, including the total baryon number, lepton number, and all the other nearly conserved pseudo-charges[clarification needed] of particle physics. This behavior is so puzzling that it has been called the black hole information loss paradox.[33][34]
Physical properties
The simplest black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to asSchwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916.[7] According to Birkhoff's theorem, it is the onlyvacuum solution that is spherically symmetric.[35] This means that there is no observable difference between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore only correct near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass.[36][unreliable source?]
Solutions describing more general black holes also exist. Charged black holes are described by the Reissner–Nordström metric, while theKerr metric describes a rotating black hole. The most general stationary black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum.[37]
While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. In Planck units, the total electric charge Q and the total angular momentum J are expected to satisfy
for a black hole of mass M. Black holes saturating this inequality are called extremal. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have so-called naked singularities that can be observed from the outside, and hence are deemed unphysical. The cosmic censorship hypothesis rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter.[38] This is supported by numerical simulations.[39]
Due to the relatively large strength of the electromagnetic force, black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a common feature of compact objects. The black-hole candidate binary X-ray source GRS 1915+105[40] appears to have an angular momentum near the maximum allowed value.
| Class | Mass | Size |
|---|---|---|
| Supermassive black hole | ~105–109 MSun | ~0.001–10 AU |
| Intermediate-mass black hole | ~103 MSun | ~103 km = REarth |
| Stellar black hole | ~10 MSun | ~30 km |
| Micro black hole | up to ~MMoon | up to ~0.1 mm |
Black holes are commonly classified according to their mass, independent of angular momentum J or electric charge Q. The size of a black hole, as determined by the radius of the event horizon, orSchwarzschild radius, is roughly proportional to the mass M through
where rsh is the Schwarzschild radius and MSun is the mass of the Sun.[41] This relation is exact only for black holes with zero charge and angular momentum; for more general black holes it can differ up to a factor of 2.
Event horizon
Main article: Event horizon
 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.[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.[43]
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.[44] 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.[45] 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.[46] At the same time, all processes on this object slow down causing emitted light to appear redder and dimmer, an effect known as gravitational redshift.[47] 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, although 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.[48]
The shape of the event horizon of a black hole is always approximately spherical.[Note 2][51] For non-rotating (static) black holes the geometry is precisely spherical, while for rotating black holes the sphere is somewhat oblated.
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.[52] 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.[53] 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.[54] The singular region can thus be thought of as having infinite density.
Observers falling into a Schwarzschild black hole (i.e. non-rotating and no charges) 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.[55] 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.[56]
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 awormhole.[57] The possibility of traveling to another universe is however only theoretical, since any perturbation will destroy this possibility.[58]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.[59] It is expected that none of these peculiar effects would survive in a proper quantum mechanical treatment of rotating and charged black holes.[60]
The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory.[61] This breakdown, however, is expected; it occurs in a situation where quantum mechanical 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. It is generally expected that a theory of quantum gravity will feature black holes without singularities.[62][63]
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.
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.[64] 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.[65]
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.[66]
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.[67] 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,[68] 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.[26] 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.[69] 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 (the ideal gas law explains the connection between pressure, temperature, and volume).[70]
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 that were over 20 solar masses before the collapse.[70]
If the mass of the remnant exceeds about 3–4 solar masses (the Tolman–Oppenheimer–Volkoff limit[13])—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.[70]
This gravitational collapse of heavy stars is assumed to be responsible for the formation of stellar mass black holes. Star formation in the young universe may have resulted in very heavy stars, which upon their collapse would have produced black holes of up to 103 solar masses. These heavy black holes could be the seeds of the supermassive black holes found in the centers of most galaxies.[71]
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.[72]
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 forprimordial 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.[73] 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.[74] 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 make the theory of general relativity break down completely.[75] 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 the Planck mass could be much lower: some braneworld scenarios for example put it much lower, maybe even as low as 1 TeV/c2[76]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.[77] Even if such micro black holes should be formed in these collisions, it is expected that they would evaporate in about 10−25seconds, posing no threat to Earth.[78]
Growth
Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas andinterstellar dust from its direct surroundings and omnipresent cosmic background radiation. This is the primary process through which supermassive black holes seem to have grown.[71] A similar process has been suggested for the formation of intermediate-mass black holesin globular clusters.[79]
Another possibility is for a black hole to merge with other objects such as stars or even other black holes. This is thought to have been important especially for the early development of supermassive black holes, which are thought to have formed from the coagulation of many smaller objects.[71] The process has also been proposed as the origin of some intermediate-mass black holes.[80][81]
Evaporation
Main article: Hawking radiation
In 1974, Hawking showed that black holes are not entirely black but emit small amounts of thermal radiation.[29] 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.[82] 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 a form of energy (E = mc2).[29] 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.[83]
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 thecosmic 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. 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).[84]
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[85] – hypothetically make such a small black hole stable.[86]
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 has proven unsuccessful and provides stringent limits on the possibility of existence of light primordial black holes.[87] NASA's Fermi Gamma-ray Space Telescope launched in 2008 will continue the search for these flashes.[88]
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.
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.[89] 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.[89] (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 thought to be the accretion discs of supermassive black holes.[90] 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.[90] It has also been suggested that some ultraluminous X-ray sources may be the accretion disks of intermediate-mass black holes.[91]
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.[90]
The first strong candidate for a black hole, Cygnus X-1, was discovered in this way byCharles Thomas Bolton[92] and Louise Webster and Paul Murdin[93] in 1972.[94][95] Some doubt, however, remained due to the uncertainties resultant from the companion star being much heavier than the candidate black hole.[90] Currently, better candidates for black holes are found in a class of X-ray binaries called soft X-ray transients.[90] 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 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.[96] 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.[89]
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.[97]
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.[98][99]
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.[100]
It is now widely accepted that the center of (nearly) every galaxy (not just active ones) contains a supermassive black hole.[101] 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. [102]
Currently, the best evidence for a supermassive black hole comes from studying the proper motionof stars near the center of our own Milky Way.[103] 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.[104] 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.[103] 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."[104]
Gravitational lensing
Further information: Gravitational lens
The deformation of spacetime around a massive object causes light rays to be deflected much like light passing through an optic lens. This phenomenon is known as gravitational lensing. Observations have been made of weak gravitational lensing, in which photons are deflected by only a few arcseconds. However, it has never been directly observed for a black hole.[105] 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 aroundSagittarius A*.[105]
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.[90]A phase of free quarks at high density might allow the existence of dense quark stars,[106] and some supersymmetric models predict the existence of Q stars.[107] Some extensions of the standard model posit the existence of preons as fundamental building blocks of quarks andleptons, which could hypothetically form preon stars.[108] 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.[90]
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).[90] 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, typically such alternatives are not stable enough to explain the supermassive black hole candidates.[90]
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 of quantum mechanical corrections. A much anticipated feature of a theory of quantum gravity is that it will not feature singularities or event horizons (and thus no black holes).[109] In recent years, much attention has been drawn by the fuzzballmodel in string theory. Based on calculations in specific situations in string theory, the proposal suggest 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.[110]
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.[111]This result, now known as the second law of black hole mechanics, is remarkably similar to thesecond 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.[112]
The link with the laws of thermodynamics was further strengthened by Hawking's discovery thatquantum field theory predicts that a black hole radiates blackbody radiation at a constant temperature. This seemingly causes a violation of the second law of black hole mechanics, since the radiation will carry away energy from the black hole causing it to shrink. The radiation, however also carries away entropy, and it can be proven under general assumptions that the sum of the entropy of the matter surrounding a black hole and one quarter of the area of the horizon as measured in Planck units is in fact always increasing. This allows the formulation of the first law of black hole mechanics as an analogue of the first law of thermodynamics, with the mass acting as energy, the surface gravity as temperature and the area as entropy.[112]
One puzzling feature is that the entropy of a black hole scales with its area rather than with its volume, since entropy is normally anextensive 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 volume of spacetime can be described by data on the boundary of that volume.[113]
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.[114] 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.[115]
Black hole unitarity
Main article: Black hole information paradox
| You Can Also See in unsolved Physics Problem |
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 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 thedensity matrix).[116]
PHYSICS PROBLEM
In physics, physical information refers generally to the information that is contained in a physical system. Its usage in quantum mechanics(i.e. quantum information) is important, for example in the concept of quantum entanglement to describe effectively direct or causalrelationships between apparently distinct or spatially separated particles.
Information itself may be loosely defined as "that which can distinguish one thing from another"[citation needed]. The information embodied by a thing can thus be said to be the identity of the particular thing itself, that is, all of its properties, all that makes it distinct from other (real or potential) things. It is a complete description of the thing, but in a sense that is divorced from any particular language.
When clarifying the subject of information, care should be taken to distinguish between the following specific cases:
- The phrase instance of information refers to the specific instantiation of information (identity, form, essence) that is associated with the being of a particular example of a thing. (This allows for the reference to separate instances of information that happen to share identical patterns.)
- A holder of information is a variable or mutable instance that can have different forms at different times (or in different situations).
- A piece of information is a particular fact about a thing's identity or properties, i.e., a portion of its instance.
- A pattern of information (or form) is the pattern or content of an instance or piece of information. Many separate pieces of information may share the same form. We can say that those pieces are perfectly correlated or say that they are copies of each other, as in copies of a book.
- An embodiment of information is the thing whose essence is a given instance of information.
- A representation of information is an encoding of some pattern of information within some other pattern or instance.
- An interpretation of information is a decoding of a pattern of information as being a representation of another specific pattern or fact.
- A subject of information is the thing that is identified or described by a given instance or piece of information. (Most generally, a thing that is a subject of information could be either abstract or concrete; either mathematical or physical.)
- An amount of information is a quantification of how large a given instance, piece, or pattern of information is, or how much of a given system's information content (its instance) has a given attribute, such as being known or unknown. Amounts of information are most naturally characterized in logarithmic units.
The above usages are clearly all conceptually distinct from each other. However, many people insist on overloading the word "information" (by itself) to denote (or connote) several of these concepts simultaneously. (Since this may lead to confusion, this article uses more detailed phrases, such as those shown in bold above, whenever the intended meaning is not made clear by the context.)
Classical versus quantum information
The instance of information that is contained in a physical system is generally considered to specify that system's "true" state. (In many practical situations, a system's true state may be largely unknown, but a realist would insist that a physical system regardless always has, in principle, a true state of some sort—whether classical or quantum.)
When discussing the information that is contained in physical systems according to modern quantum physics, we must distinguish between classical information and quantum information. Quantum information specifies the complete quantum state vector (or equivalently, wavefunction) of a system, whereas classical information, roughly speaking, only picks out a definite (pure) quantum state if we are already given a prespecified set of distinguishable (orthogonal) quantum states to choose from; such a set forms a basis for the vector space of all the possible pure quantum states (see pure state). Quantum information could thus be expressed by providing (1) a choice of a basis such that the actual quantum state is equal to one of the basis vectors, together with (2) the classical information specifying which of these basis vectors is the actual one. (However, the quantum information by itself does not include a specification of the basis, indeed, an uncountable number of different bases will include any given state vector.)
Note that the amount of classical information in a quantum system gives the maximum amount of information that can actually be measured and extracted from that quantum system for use by external classical (decoherent) systems, since only basis states are operationally distinguishable from each other. The impossibility of differentiating between non-orthogonal states is a fundamental principle of quantum mechanics[citation needed], equivalent to Heisenberg's uncertainty principle[citation needed]. Because of its more general utility, the remainder of this article will deal primarily with classical information, although quantum information theory does also have some potential applications (quantum computing, quantum cryptography, quantum teleportation) that are currently being actively explored by both theoreticians and experimentalists.[1]
[edit]Quantifying classical physical information
An amount of (classical) physical information may be quantified, as in information theory, as follows.[2] For a system S, defined abstractly in such a way that it has N distinguishable states (orthogonal quantum states) that are consistent with its description, the amount of informationI(S) contained in the system's state can be said to be log(N). The logarithm is selected for this definition since it has the advantage that this measure of information content is additive when concatenating independent, unrelated subsystems; e.g., if subsystem A has Ndistinguishable states (I(A) = log(N) information content) and an independent subsystem B has M distinguishable states (I(B) = log(M) information content), then the concatenated system has NM distinguishable states and an information content I(AB) = log(NM) = log(N) + log(M) = I(A) + I(B). We expect information to be additive from our everyday associations with the meaning of the word, e.g., that two pages of a book can contain twice as much information as one page.
The base of the logarithm used in this definition is arbitrary, since it affects the result by only a multiplicative constant, which determines the unit of information that is implied. If the log is taken base 2, the unit of information is the binary digit or bit (so named by John Tukey); if we use a natural logarithm instead, we might call the resulting unit the "nat." In magnitude, a nat is apparently identical to Boltzmann's constantk or the ideal gas constant R, although these particular quantities are usually reserved to measure physical information that happens to be entropy, and that are expressed in physical units such as joules per kelvin, or kilocalories per mole-kelvin.
[edit]Physical information and entropy
An easy way to understand the underlying unity between physical (as in thermodynamic) entropy and information-theoretic entropy is as follows: Entropy is simply that portion of the (classical) physical information contained in a system of interest (whether it is an entire physical system, or just a subsystem delineated by a set of possible messages) whose identity (as opposed to amount) is unknown (from the point of view of a particular knower). This informal characterization corresponds to both von Neumann's formal definition of the entropy of a mixed quantum state (which is just a statistical mixture of pure states; see von Neumann entropy), as well as Claude Shannon's definition of the entropy of a probability distribution over classical signal states or messages (see information entropy).[2] Incidentally, the credit for Shannon's entropy formula (though not for its use in an information theory context) really belongs to Boltzmann, who derived it much earlier for use in hisH-theorem of statistical mechanics.[3] (Shannon himself references Boltzmann in his monograph.[2])
Furthermore, even when the state of a system is known, we can say that the information in the system is still effectively entropy if that information is effectively incompressible, that is, if there are no known or feasibly determinable correlations or redundancies between different pieces of information within the system. Note that this definition of entropy can even be viewed as equivalent to the previous one (unknown information) if we take a meta-perspective, and say that for observer A to "know" the state of system B means simply that there is a definite correlation between the state of observer A and the state of system B; this correlation could thus be used by a meta-observer (that is, whoever is discussing the overall situation regarding A's state of knowledge about B) to compress his own description of the joint systemAB.[4]
Due to this connection with algorithmic information theory,[5] entropy can be said to be that portion of a system's information capacity which is "used up," that is, unavailable for storing new information (even if the existing information content were to be compressed). The rest of a system's information capacity (aside from its entropy) might be called extropy, and it represents the part of the system's information capacity which is potentially still available for storing newly derived information. The fact that physical entropy is basically "used-up storage capacity" is a direct concern in the engineering of computing systems; e.g., a computer must first remove the entropy from a given physical subsystem (eventually expelling it to the environment, and emitting heat) in order for that subsystem to be used to store some newly computed information.[4]
[edit]Extreme physical information
Main article: Extreme physical information
According to a theory developed by B. Roy Frieden,[6][7][8][9] "physical information" can be defined to be the loss of Fisher information that is incurred during the observation of a "physical effect".
Frieden states, if the effect has an intrinsic information level J, and is observed with information level I, then the physical information is defined to be the difference I − J, which Frieden calls the information Lagrangian. Frieden's so-called principle of extreme physical information or EPI states that extremalizing I − J with respect to variation of the system probability amplitudes can be used the correct Lagrangians for most or even all physical theories.
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