# Black hole: Wikis

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Simulated view of a black hole in front of the Large Magellanic Cloud. The ratio between the black hole Schwarzschild radius and the observer distance to it is 1:9. Of note is the gravitational lensing effect known as an Einstein ring, which produces a set of two fairly bright and large but highly distorted images of the Cloud as compared to its actual angular size.
General relativity
$G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}$
Einstein field equations
Introduction
Mathematical formulation
Resources
Phenomena
Kepler problem · Lenses · Waves
Frame-dragging · Geodetic effect
Event horizon · Singularity
Black hole

According to the general theory of relativity, a black hole is a region of space from which nothing, including light, can escape. It is the result of the deformation of spacetime caused by a very compact mass. Around a black hole there is an undetectable surface which marks the point of no return, called an event horizon. It is called "black" because it absorbs all the light that hits it, reflecting nothing, just like a perfect black body in thermodynamics.[1] Under the theory of quantum mechanics black holes possess a temperature and emit Hawking radiation.

Despite its invisible interior, a black hole can be observed through its interaction with other matter. A black hole can be inferred by tracking the movement of a group of stars that orbit a region in space. Alternatively, when gas falls into a stellar black hole from a companion star, the gas spirals inward, heating to very high temperatures and emitting large amounts of radiation that can be detected from earthbound and Earth-orbiting telescopes.

Astronomers have identified numerous stellar black hole candidates, and have also found evidence of supermassive black holes at the center of galaxies. After observing the motion of nearby stars for 16 years, in 2008 astronomers found compelling evidence that a supermassive black hole of more than 4 million solar masses is located near the Sagittarius A* region in the center of the Milky Way galaxy.

## History

Simulation of Gravitational lensing by a black hole which distorts the image of a galaxy in the background. (Click for larger animation.)

The idea of a body so massive that even light could not escape was first put forward by geologist John Michell in a letter written to Henry Cavendish in 1783 to 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[2]

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).[3][4] Such "dark stars" were largely ignored in the nineteenth century, since light was then thought to be a massless wave and therefore not influenced by gravity. Unlike the modern black hole concept, the object behind the horizon of a dark star is assumed to be stable against collapse.

### General relativity

In 1915, Albert Einstein developed his general theory of relativity, having earlier shown that gravity does influence light's motion. A few months later, Karl Schwarzschild gave the solution for the gravitational field of a point mass and a spherical mass,[5] showing that a black hole could theoretically exist. The Schwarzschild radius is now known to be the radius of the event horizon of a non-rotating black hole, but this was not well understood then and Schwarzschild himself thought it was not physical. Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass a few months after Schwarzschild and wrote more extensively about its properties.

In 1930, astrophysicist Subrahmanyan Chandrasekhar calculated, using general relativity, that a non-rotating body of electron-degenerate matter above 1.44 solar masses (the Chandrasekhar limit) would collapse. His arguments were opposed by Arthur Eddington, who believed that something would inevitably stop the collapse. Eddington was partly correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star, which is itself stable because of the Pauli exclusion principle. But in 1939, Robert Oppenheimer and others predicted that stars above approximately three solar masses (the Tolman-Oppenheimer-Volkoff limit) would collapse into black holes for the reasons presented by Chandrasekhar.[6]

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 some of the terms in the equations became infinite at the Schwarzschild radius. This was interpreted as indicating that the Schwarzschild radius 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,"[7] 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. This is a known property of modern black holes, but it must be emphasized that the light from the surface of the frozen star becomes redshifted very fast, turning the black hole black very quickly. Many physicists could not accept the idea of time standing still at the Schwarzschild radius, and there was little interest in the subject for over 20 years.

### Golden age

In 1958, David Finkelstein introduced the concept of the event horizon by presenting Eddington-Finkelstein coordinates, which enabled him to show that "The Schwarzschild surface r = 2 m is not a singularity, but that it acts as a perfect unidirectional membrane: causal influences can cross it in only one direction".[8] This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. All theories up to this point, including Finkelstein's, covered only non-rotating black holes. In 1963, Roy Kerr found the exact solution for a rotating black hole. Two years later, Roger Penrose was able to prove that singularities occur inside any black hole.[9] In 1967, astronomers discovered pulsars,[10][11] 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.

Physicist John Wheeler is widely credited with coining the term black hole in his 1967 public lecture Our Universe: the Known and Unknown, as an alternative to the more cumbersome "gravitationally completely collapsed star." However, Wheeler insisted that someone else at the conference had coined the term and he had merely adopted it as useful shorthand. The term was also cited in a 1964 letter by Anne Ewing to the AAAS:

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.
—Ann Ewing, letter to AAAS[12]

## 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.[13] Any two black holes that share the same values for these properties, or parameters, are classically indistinguishable.

These properties are special because they are visible from outside the 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.[14] Likewise, the angular momentum can be measured from far away using frame dragging by the gravitomagnetic field.

When a black hole swallows any form of matter, its horizon oscillates like a stretchy membrane with friction, a dissipative system, until it reaches a simple final state (see membrane paradigm).[15] Similarly, any information about the charge distribution of the matter is lost as the field is evenly distributed along the event horizon as if the black hole was acting like a conducting sphere with a definite resistivity. This is different from other field theories like electromagnetism, which does not have any friction or resistivity at the microscopic level, because they are time reversible. Because the 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 the 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 of particle physics. This behavior is so puzzling, that it has been called the black hole information loss paradox.[16][17][18]

### Classification

#### By physical properties

The simplest black hole has mass but neither charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after the physicist Karl Schwarzschild who discovered this solution in 1915.[5] It was the first non-trivial exact solution to the Einstein field equations to be discovered, and according to Birkhoff's theorem, the only vacuum solution that is spherically symmetric.[19] 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 the black hole horizon; far away, the external gravitational field is identical to that of any other body of the same mass.[20]

More general black hole solutions were discovered later in the 20th century. The Reissner-Nordström metric describes a black hole with electric charge, while the Kerr metric yields a rotating black hole. The more generally known stationary black hole solution, the Kerr-Newman metric, describes both charge and angular momentum.

While the mass of a black hole can take any positive value, the 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

$Q^2+\left ( \tfrac{J}{M} \right )^2\le M^2\,$

for a black hole of mass M.

Black holes saturating this inequality are called extremal. Solutions of Einstein's equations violating the inequality do exist, but do not have a horizon. These solutions have naked singularities and are deemed unphysical, as the cosmic censorship hypothesis rules out such singularities due to the generic gravitational collapse of realistic matter.[21] This is supported by numerical simulations.[22]

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, and the black-hole candidate binary X-ray source GRS 1915+105[23] appears to have an angular momentum near the maximum allowed value.

#### By mass

Class Mass Size
Supermassive black hole ~105–109 MSun ~0.001–10 AU
Intermediate-mass black hole ~103 MSun ~103 km = REarth
Stellar-mass ~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 $J\,$. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is proportional to the mass $M\,$ through

$r_{sh} \approx 2.95\, M/M_\bigodot \;\mathrm{km,}$

where $r_{sh}\,$ is the Schwarzschild radius and $M_\bigodot$ is the mass of the Sun. A black hole's size and mass are thus simply related independent of rotation. According to this criterion, black holes are classed as:

• Supermassive – contain hundreds of thousands to billions of solar masses, and are thought to exist in the center of most galaxies,[24][25] including the Milky Way.[26] They are thought to be responsible for active galactic nuclei, and presumably form either from the coalescence of smaller black holes, or by the accretion of stars and gas onto them. The largest known supermassive black hole is located in OJ 287 weighing in at 18 billion solar masses.[27]
• Intermediate – contain thousands of solar masses. They have been proposed as a possible power source for ultraluminous X-ray sources.[28] There is no known mechanism for them to form directly, so they likely form by collisions of lower mass black holes, either in the dense stellar cores of globular clusters or galaxies.[citation needed] Such creation events should produce intense bursts of gravitational waves, which may be observed soon. The boundary between super- and intermediate-mass black holes is a matter of convention. Their lower mass limit, the maximum mass for direct formation of a single black hole from collapse of a massive star, is poorly known at present, but is thought to be somewhere well below 200 solar masses.
• Stellar-mass – have masses ranging from a lower limit of about 1.4–3 solar masses (1.4 is the Chandrasekhar limit and 3 is the Tolman-Oppenheimer-Volkoff limit for the maximum mass of neutron stars) up to perhaps 15–20 solar masses. They are created by the collapse of individual stars, or by the coalescence (inevitable, due to gravitational radiation) of binary neutron stars. Stars may form with initial masses up to about 100 solar masses, or in the distant past, possibly even higher, but these shed most of their outer massive layers during earlier phases of their evolution, either blown away in stellar winds during the red giant, AGB, and Wolf-Rayet stages, or expelled in supernova explosions for stars that turn into neutron stars or black holes. Being known mostly by theoretical models for late-stage stellar evolution, the upper limit for the mass of stellar-mass black holes is somewhat uncertain at present. The cores of still lighter stars form white dwarfs.

### 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. 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, including light, can escape from inside the event horizon. The event horizon is referred to as such because if an event occurs within the boundary, light from that event cannot reach an outside observer, making it impossible to determine if such an event occurred.[30]

As predicted by general relativity, the presence of a large mass deforms spacetime in such a way that the paths particles take bend towards the mass. 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.[31]

To a distant observer, clocks near a black hole appear to tick more slowly than those further away from the black hole.[32] 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.[33] 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.[34] 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.[35]

For a non rotating (static) black hole, the Schwarzschild radius delimits a spherical event horizon. The Schwarzschild radius of an object is proportional to the mass.[36] Rotating black holes have distorted, nonspherical event horizons. Since the event horizon is not a material surface but rather merely a mathematically defined demarcation boundary, nothing prevents matter or radiation from entering a black hole, only from exiting one. The description of black holes given by general relativity is known to be an approximation, and it is expected that quantum gravity effects become significant near the vicinity of the event horizon.[37] This allows observations of matter near a black hole's event horizon to be used to indirectly study general relativity and proposed extensions to it.

### 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.[38] 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 shape lying in the plane of rotation.[39] 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.[40] The singular region can thus be thought of as having infinite density.

An observer falling into a Schwarzschild black hole (i.e. non-rotating and no charges) cannot avoid the singularity. Any attempt to do so will only shorten the time taken to get there.[41] When he reaches the singularity he is crushed to infinite density and his mass is added to the total of the black hole. Before that happens he will have been torn apart by the growing tidal forces in a process sometimes referred to as spaghettification or the noodle effect.[42]

In the case of a charged (Reissner-Nordström) or rotating (Kerr) black hole it is possible to avoid the singularity. Extending these solutions as far as possible reveals the hypothetical possibility of exiting the black hole into a different spacetime with the black hole acting as a worm hole.[43] It also appears to be possible to follow closed timelike curves around the Kerr singularity, which lead to problems with causality like the grandfather paradox.[44] It is expected that none of these peculiar effects would survive in a proper quantum mechanical treatment of rotating and charged black holes.[45]

The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory.[46] 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.[47][48]

### 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.[49] 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

The ergosphere is an oblate spheroid region outside of the event horizon, where objects cannot remain stationary.

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.[50]

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.[51]

## 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.[52] 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,[53] 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.[9] Shortly afterwards, Stephen 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.[54] 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 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).[55]

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.[55]

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.[55]

This gravitational collapse of heavy stars is assumed to be responsible for the formation of most (if not all) stellar mass black holes.[citation needed]

While most of the energy released during gravitational collapse is emitted very quickly, an outside observer doesn't 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 horison, 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.[56]

#### 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.[57] Primordial black holes could thus account for the creation of any type of black hole.

### High energy collisions

A simulated event in the CMS detector, a collision in which a micro black hole may be created.

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.[58] 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.[59] 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, maybe even as low as 1 TeV/c2.[60] 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 is 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.[61] 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.[62] 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).[61] 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. 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 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.[63] NASA's Fermi Gamma-ray Space Telescope launched in 2008 will continue the search for these flashes.[64]

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

Formation of extragalactic jets from a black hole's accretion disk

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.[65] 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.[65] (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, 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.[66] 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.[66] It has also been suggested that some ultraluminous X-ray sources may be the accretion disks of intermediate-mass black holes.[67]

### 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.

Artist impression of a binary system with an accretion disk around a compact object being fed by material from the companion star.

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.[66]

The first strong candidate for a black hole, Cygnus X-1, was discovered in this way by Webster and Murdin[68] and Bolton[69] in 1972.[70][71] Some doubt, however, remained due to the uncertainties resultant from the companion star being much heavier than the candidate black hole.[66] Currently, better candidates for black holes are found in a class of X-ray binaries called soft X-ray transients.[66] 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 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. 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.[65]

#### 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.[72]

### 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[73] or by collisions between neutron stars,[74] and both types of event involve sufficient mass and pressure to produce black holes. It appears that a collision between a neutron star and a black hole can also cause a GRB,[75] 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[76] so the black holes associated with them are billions of years old.

### Galactic nuclei

The jet originating from the center of M87 in this image comes from an active galactic nucleus that may contain a supermassive black hole. Credit: Hubble Space Telescope/NASA/ESA.

It is now widely accepted that the center of every or at least nearly every galaxy contains a supermassive black hole.[77][78] 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.[77]

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.[79][80] However, theoretical and observational studies have shown that the active galactic nuclei (AGN) in these galaxies may contain supermassive black holes.[79][80] 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.[80]

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.[81]

Currently, the best evidence for a supermassive black hole comes from the center of our own Milky way.[82] For sixteen years astronomers have tracked the positions of stars orbiting a central massive object in a region called Sagittarius A*, one of which—a 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.[82] 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.

### Gravitational lensing

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.[83] One possibility for observing gravitational lensing by a black hole would be to observe stars in orbit around the black hole. There are several candidates for such an observation in orbit around Sagittarius A*.[83]

### 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.[66] A phase of free quarks at high density might allow the existence of dense quark stars,[84] and some supersymmetric models predict the existence of Q stars.[85] Some extensions of the standard model posit the existence of preons as fundamental building blocks of quarks and leptons which could hypothetically form preon stars.[86] 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.[66]

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 large supermassive black hole is comparable to that of water).[66] 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.[66]

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).[citation needed] In recent years, much attention has been drawn by the fuzzball model 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 (and can thus not really be considered to be a black hole), but that for a distant observer the statistical average of such states does appear just like an ordinary black hole in general relativity.[87]

## Open questions

If ultra-high-energy collisions of particles in a particle accelerator can create microscopic black holes, it is expected that all types of particles will be emitted by black hole evaporation, providing key evidence for any grand unified theory. Above are the high energy particles produced in a gold ion collision on the RHIC.

In 1971, Stephen Hawking showed under general conditions[Note 1] 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.[88] This result now known as the second law of black hole mechanics is remarkably similar to the Second Law of Thermodynamics, which states that the total entropy of a system can never decrease. As 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.[citation needed]

The link with the laws of thermodynamics was further strengthened by the discovery of Hawking's discovery that quantum field theory predicts that a black hole radiates blackbody radiation at a constant temperature.[citation needed] 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 the black hole and one quarter of the area of the horizon as measured in planck units is in fact always increasing.[citation needed] 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.[citation needed]

One puzzling feature is that the entropy of a black hole scales with its area rather than with its volume. Since entropy is normally an extrinsic property that scales linearly with the volume of the system. This odd property led 't Hooft and 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.[citation needed]

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.). 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).[89]

## Notes

1. ^ In particular, he assumed that all matter satisfies the weak energy condition.

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• Ferguson, Kitty (1991). Black Holes in Space-Time. Watts Franklin. ISBN 0-531-12524-6. .
• Hawking, Stephen (1988). A Brief History of Time. Bantam Books, Inc. ISBN 0-553-38016-8. .
• Hawking, Stephen; Penrose, Roger (1996). The Nature of Space and Time. Princeton University Press. ISBN 0-691-03791-2. .
• Melia, Fulvio (2003). The Black Hole at the Center of Our Galaxy. Princeton U Press. ISBN 978-0-691-09505-9. .
• Melia, Fulvio (2003). The Edge of Infinity. Supermassive Black Holes in the Universe. Cambridge U Press. ISBN 978-0-521-81405-8. .
• Pickover, Clifford (1998). Black Holes: A Traveler's Guide. Wiley, John & Sons, Inc. ISBN 0-471-19704-1. .
• Stern, B. (2008). "Blackhole". , poem.
• Thorne, Kip S. (1994). Black Holes and Time Warps. Norton, W. W. & Company, Inc. ISBN 0-393-31276-3. .
• Wheeler, J. Craig (2007). Cosmic Catastrophes (2nd ed.). Cambridge University Press. ISBN 0-521-85714-7.

### University textbooks and monographs

• Carroll, Sean M. (2004). Spacetime and Geometry. Addison Wesley. ISBN 0-8053-8732-3. , the lecture notes on which the book was based are available for free from Sean Carroll's website.
• Carter, B. (1973). "Black hole equilibrium states". in DeWitt, B.S.; DeWitt, C.. Black Holes. .
• Chandrasekhar, Subrahmanyan (1999). Mathematical Theory of Black Holes. Oxford University Press. ISBN 0-19-850370-9. .
• Frolov, V.P.; Novikov, I.D. (1998). Black hole physics. .
• Hawking, S.W.; Ellis, G.F.R. (1973). Large Scale Structure of space time. Cambridge University Press. ISBN 0521099064. .
• Melia, Fulvio (2007). The Galactic Supermassive Black Hole. Princeton U Press. ISBN 978-0-691-13129-0. .
• Taylor, Edwin F.; Wheeler, John Archibald (2000). Exploring Black Holes. Addison Wesley Longman. ISBN 0-201-38423-X. .
• Thorne, Kip S.; Misner, Charles; Wheeler, John (1973). Gravitation. W. H. Freeman and Company. ISBN 0-7167-0344-0. .
• Wald, Robert M. (1992). Space, Time, and Gravity: The Theory of the Big Bang and Black Holes. University of Chicago Press. ISBN 0-226-87029-4. .

### Research papers

• Hawking, S. (2005). "Information loss in black holes". Physical Review D 72: 084013. doi:10.1103/PhysRevD.72.084013. arΧiv:hep-th/0507171v2.  Stephen Hawking's purported solution to the black hole unitarity paradox, first reported at a conference in July 2004.
• Ghez, A. M.; Salim, S.; Hornstein, S. D.; Tanner, A.; Lu, J. R.; Morris, M.; Becklin, E. E.; Duchene, G. (2005). "Stellar Orbits around the Galactic Center Black Hole". The Astrophysical Journal 620: 744. doi:10.1086/427175. arΧiv:astro-ph/0306130v2.  More accurate mass and position for the black hole at the centre of the Milky Way.
• Hughes, Scott A. (2005). "Trust but verify: The case for astrophysical black holes". arΧiv:hep-ph/0511217v2 [hep-ph].  Lecture notes from 2005 SLAC Summer Institute.

# Study guide

Up to date as of January 14, 2010

### From Wikiversity

A black hole is a theoretical region of space that has such a strong gravity pull that not even light can escape it. It is called black because it sucks in all light, reflecting nothing, therefore appearing "black". Though it is not possible to see one, a black hole's location can be inferred by observing any celestial bodies that orbit an apparently empty space.

## Terminology

A black hole is often referred to as any object whose escape velocity exceeds the speed of light.

The escape velocity is the speed at which an object needs to travel so as to just manage to get infinitely far away from a source of gravity before stopping. On the Earth, the escape velocity is equal to 11 km/s, so no matter what the object is, a rocket or a baseball, it must go at least 11 km/s to avoid falling back to the Earth's surface eventually. Light passing by a black hole would be sucked in, it it came close enough.

## Event horizon

The event horizon is a region of spacetime that cannot affect an outside observer in any way. Coming close to the black hole, an objects movement is encouraged to move towards the event horizon. If the object crosses the event horizon, then any possible movement would just pull it deeper.

## Wikimedia

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# Simple English

General relativity
$G_\left\{\mu \nu\right\} + \Lambda g_\left\{\mu \nu\right\}= \left\{8\pi G\over c^4\right\} T_\left\{\mu \nu\right\}$
Einstein field equations
Introduction
Mathematical formulation
Resources
Phenomena
Kepler problem · Lenses · Waves
Frame-dragging · Geodetic effect
Event horizon · Singularity
Black hole
File:Black Hole
This image is a simulation of what a black hole might look like. No black hole has ever been photographed.

According to the general theory of relativity, a black hole is a region of space from which nothing, including light, can escape. It is the result of the denting of spacetime caused by a very compact mass. Around a black hole there is an undetectable surface which marks the point of no return, called an event horizon. It is called "black" because it absorbs all the light that hits it, reflecting nothing, just like a perfect black body in thermodynamics.[1] Under the theory of quantum mechanics black holes possess a temperature and emit Hawking radiation.

Despite its invisible interior, a black hole can be observed through its interaction with other matter. A black hole can be inferred by tracking the movement of a group of stars that orbit a region in space. Alternatively, when gas falls into a stellar black hole from a companion star, the gas spirals inward, heating to very high temperatures and emitting large amounts of radiation that can be detected from earthbound and Earth-orbiting telescopes.

Astronomers have identified numerous stellar black hole candidates, and have also found evidence of supermassive black holes at the center of galaxies. After observing the motion of nearby stars for 16 years, in 2008 astronomers found compelling evidence that a supermassive black hole of more than 4 million solar masses is located near the Sagittarius A* region in the center of the Milky Way galaxy.

## History

In 1783, an English geologist named John Mitchell wrote that it might be possible for something to be so big and heavy that the escape speed from its gravity is equal to the speed of light. Gravity gets stronger as something gets bigger or more massive. For a small thing, like a rocket, to escape from a larger thing, like Earth, it has to go upward very fast or it will fall back down later. The speed that it must travel upward to get away from Earth's gravity is called escape velocity. Bigger planets (like Jupiter) and stars have stronger gravity than Earth, so the escape velocity is much faster. John Mitchell thought it was possible for something to be so big that the escape velocity would be faster than the speed of light, so even light could not escape.

Some scientists thought Mitchell might be right, but others thought that light had no mass and would not be pulled by gravity. His theory was forgotten.

In 1916, Albert Einstein wrote an explanation of gravity called general relativity. It is a very complicated theory, but there are two important things about it:

• Mass causes space (and spacetime) to bend, or curve. Moving things "fall along" or follow the curves in space. This is what we call gravity.
• Light always travels at the same speed, and is affected by gravity. If it seems to change speed, it is really traveling along a curve in spacetime.

A few months later, a German physicist named Karl Schwarzschild calculated that a black hole could exist.

In 1930, Subrahmanyan Chandrasekhar predicted that stars heavier than the sun could collapse when they ran out of hydrogen to burn and died. In 1939, Robert Oppenheimer and H. Snyder calculated that a star would have to be at least three times as massive as the sun to form a black hole.

In 1967, John Wheeler gave black holes the name "black hole" for the first time. Before that, they were called "dark stars."

In 1970, Stephen Hawking and Roger Penrose proved that black holes must exist. Although the black holes are invisible (they cannot be seen), some of the matter that is falling into them is very bright.

## Formation of black holes

Most black holes are made when a giant star, called a supergiant, at least twenty times bigger than our own Sun dies, and leaves behind a mass that is at least one solar mass. Stars die when they run out of hydrogen or other fuel to burn and start to collapse.

A supergiant star's death is called a supernova. Stars are usually in equilibrium, which means they are making enough energy to push their mass outward against the force of gravity. When the star runs out of energy, gravity takes over. Gravity pulls the center of the star inward very quickly (so quickly that it would have to be repeated several thousand times before it took up a single second), and it collapses into a little ball. The collapse is so fast and violent that it makes a shock wave, and that causes the rest of the star to explode outward. As the gravity pushes the star inward, the pressure in the center of star reaches to such an extreme level that it enables heavier molecules like iron and carbon to interact to release nuclear energy. The release of the energy from the star during a very short period of time (about one hour) is with such a high rate that it outshines an entire galaxy.

The ball in the center is so dense (a lot of mass in a small space, or volume), that if you could somehow scoop only one teaspoon of material and bring it to Earth, it would sink to the core of the planet. If the original star was large enough the densely packed ball is called a singularity, the core of a black hole, but if it was not it would become either a neutron star or a dwarf star.

Even without a supernova, a black hole will form any time there is a lot of matter in a small space, without enough energy to act against gravity and stop it from collapsing.

If supernovas are so bright, why do we not see them often? Actually, there are usually hundreds of years between naked-eye super nova sightings. It is because the period of being a super nova in a star life cycle is only a few hours out of the billions of years in a star's life span. The probability (chance) of looking at a star in sky and that being in super nova state is equal to the ratio of an hour over several billion years.

It is worth mentioning that all of the heavier materials like carbon, oxygen, all the metals, etc, that make the life on the earth possible and are ingredients of all living creatures, can only form in the extreme pressure at the center of a super nova. So we are all a remnant ash from one exploding star several billion years ago.

Black holes have also been found in the middle of every major galaxy in the universe. These are called supermassive black holes, and are the biggest black holes of all. They formed when the Universe was very young, and also helped to form all the galaxies.

Some black holes are also responsible for making things called quasars. A quasar occurs when a black hole consumes all the gas surrounding it. As the gas gets close to the black hole itself, it heats up from a process called friction, and glows so brightly that this light can be seen on the other side of the Universe. It is often brighter than the whole galaxy the quasar is in. When astronomers first found quasars, they thought they had found objects close to us. After using a measuring technique called red shift, they discovered these quasars were actually very far away in the universe.

## What black holes look like

At the middle of a black hole, there is a really small thing called a singularity, but it is impossible to see it because light gets sucked into it, and not reflected. Around the tiny singularity, there is a large area where light which would normally pass by gets sucked in as well. The edge of this area is called the event horizon. The gravity of the black hole gets weaker at a distance. The event horizon is the place farthest away from the middle where the gravity is still strong enough to trap light. The singularity is like the pipe under a sink, while the event horizon is like the edge of the drain where water always gets sucked in.

File:Accretion
A black hole pulling off the outer layer of a nearby star. It is surrounded by an energy disk, which is making a jet of radiation

Outside the event horizon, light and matter will still be pulled toward the black hole. If a black hole is surrounded by matter, the matter will form an "accretion disk" (accretion means "gathering") around the black hole. An accretion disk looks something like the rings of Saturn. As it gets sucked in, the matter gets very hot and shoots x-ray radiation into space. Think of this as the water spinning around the hole before it falls in.

Most black holes are too far away and small to see the accretion disk and jet. The best way to know a black hole is there is by seeing how stars, gas and other things behave around it. With a black hole nearby, even objects as big as a star move in a different way, usually faster than they would if the black hole was not there.

Also, because black holes can bend light passing by, if a black hole passes between us and a source of light very far away, the light will become quite distorted, like a fun-house mirror at a circus, until the black hole moves out of the way. The light can also be magnified, like a magnifying glass, allowing scientists to see things farther away (this is called gravity lensing).

We cannot actually see black holes; one way of detecting them is to look at the sky when a black hole passes between us and a source of light, the light bends around the black hole creating a mirror image, so when astronomers see patches of sky that are identical, they may have found a black hole.

A lot of science fiction writers use black holes in their stories, and many scientists wish to find one relatively close to Earth to study one better.

Scientists also think black holes might cause wormholes, theoretical "portals" through space.

## Singularities

Singularities are what scientists believe to be inside of a black hole. These singularities present a huge problem to black hole theorists because they present fundamental flaws in Einstein's work. This is because when you use the equations to work out what a singularity is, the answer is infinite time and space, which makes no scientific sense.

It was commonly thought that a black hole was there forever and if you were trapped in one, you would be stuck there eternally. This was proved wrong when scientists discovered small leaks in black holes. This meant that over billions and billions of years, a black hole would disperse. The leaking is slow at first, but as it gets smaller, it gets faster and faster.

## Black hole evaporation

Stephen Hawking discovered the evaporation of the black hole. He discovered this by 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.

## References

1. Davies, P. C. W. (1978). "Thermodynamics of Black Holes". Rep. Prog. Phys. 41: 1313–1355.

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