Black hole

For other uses, see Black hole (disambiguation).

Simulated view of a black hole in front of the Milky Way. The hole has 10 solar masses and is viewed from a distance of 600 km.

In general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, including light, can escape its pull. The black hole has a one-way surface, called the event horizon, into which objects can fall, but out of which nothing can come out. The reason it is called black is because it absorbs all the light that hits it, reflecting nothing, just like a perfect blackbody in thermodynamics.

Despite its invisible interior, a black hole can reveal its presence through 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 which looks empty. Alternatively, one can see gas falling into a relatively small black hole, from a companion star. This gas spirals inward, heating up to very high temperature and emitting large amounts of radiation that can be detected from earthbound and earth-orbiting telescopes. Such observations have resulted in the general scientific consensus that, barring a breakdown in our understanding of nature, black holes do exist in our universe.

Introduction and terminology

A black hole is often defined as an object whose escape velocity exceeds the speed of light.

The escape velocity is the speed that an object needs to go at 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. To calculate the escape velocity in Newtonian mechanics, consider a heavy object of mass M centered at the origin. A second object with mass m starting at distance r from the origin with speed v, trying to escape to infinity, needs to have just enough kinetic energy to make up for the negative gravitational potential energy, with nothing left over:

${mv^{2} \over 2}-{GMm \over r}=0$

That way, as it gets closer to $\scriptstyle r=\infty$ it has less and less kinetic energy, finally ending up at infinity with no speed.

This relation gives the critical escape velocity v in terms of M and r. But it also says that for each value of v and M, there is a critical value of r so that a particle with speed v is just able to escape:

$r={2GM \over v^{2}}$

when the velocity is equal to the speed of light, this gives the radius of a Newtonian dark star, a Newtonian body from which a particle moving at the speed of light can not escape. In the most commonly used convention for the value of the radius of a black hole, the radius of the event horizon is equal to this Newtonian value.

$r_{\rm {Schwartzschild}}={2GM \over c^{2}}$

In general relativity, the coordinate r is not completely straightforward to define, because space-time is curved, and you can choose different coordinates. For this result to be true, the value of r should be defined so that the surface area A of a sphere of radius r in the curved space time is still given by the formula $A=4\pi r^{2}$. This definition of r only makes sense when the gravitational field is spherically symmetric, so that there are concentric spheres on which the gravitational field is constant.

The escape velocity of an object depends on how compact it is; that is, the ratio of its mass to radius. A black hole forms when an object is so compact that, within a certain distance of it, even the speed of light is not fast enough to escape.

In general relativity, the black hole's mass can be thought of as concentrated at a singularity, which can be a point, a ring, a light-ray, or a sphere, the exact details are not currently well understood. Surrounding the singularity is a spherical surface called the event horizon. The event horizon marks the 'point of no return', a boundary that, if crossed, inevitably leads falling matter and radiation inwards, towards the singularity. The radius of this sphere is the size of the black hole, and is equal to twice the mass in units where G and c equal 1.

The radius of a black hole of mass equal to that of the Sun is about 3 km. At distances much larger than this, the black hole has the exact same total gravitational attraction as any other body of the same mass, just like the sun. So if the sun were replaced by a black hole of the same mass, the orbits of the planets would remain unchanged.

There are several types of black holes, characterized by their typical size. When they form as a result of the gravitational collapse of a star, they are called stellar black holes. Black holes found at the center of galaxies have a mass up to several billion solar masses and are called supermassive black holes, because they are so big. Between these two scales, there are believed to be intermediate black holes with a mass of several thousand solar masses. Black holes with very small masses, believed to have formed early in the history of the Universe, during the Big Bang, might also exist, and are referred to as primordial black holes. Their existence is, at present, not confirmed.

It is impossible to directly observe a black hole. However, it is possible to infer its presence by its gravitational action on the surrounding environment, particularly with microquasars and active galactic nuclei, where material falling into a nearby black hole is significantly heated and emits a large amount of X-ray radiation. This observation method allows astronomers to detect their existence. The only objects that agree with these observations and are consistent within the framework of general relativity are black holes.

History

Simulation of Gravitational lensing by a black hole which distorts a galaxy in the background.

The idea of a body so massive that even light could not escape was 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

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). 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 is assumed to be stable against collapse.

In 1915, Albert Einstein developed his general theory of relativity, having earlier shown that gravity does in fact 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, 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 at that time, for example 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 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. 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.

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 Schwartschild 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 briefly known as "frozen stars", 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.

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". 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. The rotating singularity of this solution was a ring, and not a point. A short while later, Roger Penrose was able to prove that singularities occur inside any black hole.

In 1967, astronomers discovered pulsars, and within a few years could show that the known pulsars were rapidly rotating neutron stars. Until that time, neutron stars were also regarded as just theoretical curiosities. So the discovery of pulsars awakened interest in all types of ultra-dense objects that might be formed by gravitational collapse.

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

Properties and features

Main article: Properties and features of black holes

The No hair theorem states that, once it settles down, a black hole has only three independent physical properties: mass, charge and angular momentum. 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, despite the fact that photons, the particles responsible for electric and magnetic forces, can't escape from the interior region. The reason is Gauss's law, the total electric flux going out of a big sphere always stays the same, and measures the total charge inside the sphere. When charge falls into a black hole, electric field lines still remain, poking out of the horizon, and these field lines remember the total charge of all the infalling matter. The electric field lines eventually spread out evenly over the surface of the black hole, settling down to a uniform field-line density on the surface. The black hole acts in this regard like a classical conducting sphere with a definite resistivity.

Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law, far away from the black hole. 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 settles down to a simple final state. This is different from other field theories like electromagnetism or gauge theory, which never have any friction or resistivity, because they are time reversible. Because the black hole eventually settles down into a final 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 tell you very little about what went in. The information that is lost includes every quantity that can't 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

The loss of information in black holes is puzzling even classically, because General Relativity is a Lagrangian theory, which superficially appears to be time reversible and Hamiltonian. But because of the horizon, a black hole is not time reversible--- matter goes in but it can't get out. The time reverse of a classical black hole has been called a white hole, although entropy considerations and quantum mechanics suggest that white holes are just the same as black holes.

The No Hair theorem makes some assumptions about the nature of our universe and the matter it contains, and other assumptions lead to different conclusions. For example, if Magnetic monopoles exist, as predicted by some theories, the magnetic charge would be a fourth parameter for a classical black hole.

Counterexamples to the no-hair theorem are known for the following cases:

1. in spacetime dimensions higher than four
2. in the presence of non-abelian Yang-Mills fields
3. For discrete gauge symmetries.
4. some non-minimally coupled scalar fields,
5. When scalars can be topologically twisted, as in the case of skyrmions
6. in modified theories of gravity, different from Einstein’s general relativity.

These exceptions are sometimes unstable, and sometimes do not lead to new conserved quantum numbers far away from the black hole. For large black holes in our apparently four-dimensional, very nearly flat universe , the theorem should hold.

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. 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. 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 essentially like that of ordinary massive bodies.

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 $Q^{2}+\left({\tfrac {J}{M}}\right)^{2}\leq M^{2}\,$ 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. This is supported by numerical simulations.

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 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, including the Milky Way. They are believed 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.

• Intermediate - contain thousands of solar masses. They have been proposed as a possible power source for ultraluminous X-ray sources. There is no known mechanism for them to form directly, so they likely form via collisions of lower mass black holes, either in the dense stellar cores of globular clusters or galaxies. 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.

• Stellar-mass - have masses ranging from a lower limit of about 1.5–3.0 solar masses (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 ≈100 solar masses, or 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.

• Micro (also mini black holes) - have masses much less than that of a star. At these sizes, quantum mechanics is expected to take effect. There is no known mechanism for them to form via normal processes of stellar evolution, but certain inflationary scenarios predict their production during the early stages of the evolution of the universe. According to some theories of quantum gravity they may also be produced in the highly energetic reaction produced by cosmic rays hitting the atmosphere or even in particle accelerators such as the Large Hadron Collider. The theory of Hawking radiation predicts that such black holes will evaporate in bright flashes of gamma radiation. NASA's Fermi Gamma-ray Space Telescope satellite (formerly GLAST) launched in 2008 is searching for such flashes.

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.

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 beyond which events cannot affect an outside observer. As predicted by general relativity, the presence of a mass deforms spacetime in such a way that the paths particles take tend towards the mass. At the event horizon of black hole this deformation becomes so strong that there are no more paths that lead away from the black hole. Once a particle is inside the horizon, moving into the hole is as inevitable as moving forward in time (and can actually be thought of as equivalent to doing so).

To a distant observer clocks near a black hole appear to tick more slowly than those further away from the black hole. Due to this effect (known as gravitational time dilation) the distant observer will see an object falling into a black hole slow down as it approaches the event horizon, taking an infinite time to reach it. At the same time all processes on this object slow down causing emitted light to appear redder and dimmer, an effect known as gravitational red shift. Eventually, the falling object becomes so dim that it can no longer be seen, at a point just before it reaches the event horizon.

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. 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. This allows observations of matter in the vicinity of a black hole's event horizon to be used to indirectly study general relativity and proposed extensions to it.

Though black holes themselves may not radiate energy, electromagnetic radiation and matter particles may be radiated from just outside the event horizon via Hawking radiation.

Singularity

Main article: Gravitational singularity

At the center of a black hole lies the singularity, where matter is crushed to infinite density, the pull of gravity is infinitely strong, and spacetime has infinite curvature. This means that a black hole's mass becomes entirely compressed into a region with zero volume. This zero-volume, infinitely dense region at the center of a black hole is called a gravitational singularity.

The singularity of a non-rotating black hole has zero length, width, and height; a rotating black hole's is smeared out to form a ring shape lying in the plane of rotation. The ring still has no thickness and hence no volume.

The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. This breakdown, 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.

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 (maybe caused by some 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. This follows from the fact gravitation field of an object does not depend on its actual size, hence any object that is smaller than 1.5 times the Schwarzschild radius corresponding to its mass will in fact have a photon sphere.

Ergosphere

Main article: Ergosphere

File:Ergosphere.svg

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.

The ergosphere of black hole is bounded by

• on the outside, an oblate spheroid, which coincides with the event horizon at the poles and is noticeably wider around the "equator". This boundary is sometimes called the "ergosurface", but it is just a boundary and has no more solidity than the event horizon. At points exactly on the ergosurface, spacetime is "dragged around at the speed of light."
• on the inside, the (outer) event horizon.

Within the ergosphere, space-time is dragged around faster than light—general relativity forbids material objects to travel faster than light (so does special relativity), but allows regions of space-time to move faster than light relative to other regions of space-time.

Objects and radiation (including light) can stay in orbit within the ergosphere without falling to the center. But they cannot hover (remain stationary, as seen by an external observer), because that would require them to move backwards faster than light relative to their own regions of space-time, which are moving faster than light relative to an external observer.

Objects and radiation can also escape from the ergosphere. In fact the Penrose process predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way, the black hole will spin more slowly and may even stop spinning eventually.

Formation and evolution

From the exotic nature of black holes, it is natural to question if such bizarre objects could actually exist in nature or that they are merely pathological solutions to Einstein's equations. Einstein himself wrongly believed that black holes would not form, because he believed that the angular momentum of collapsing particles would stabilize their motion at some radius.. This led the general relativity community to dismiss all results to the contrary for many years.

But a minority of relativists continued to believe that black holes were physical objects, and by the end of the 1960's, they had persuaded the majority of researchers in the field that there is no obstacle to forming an event horizon.

Once an event horizon forms, Roger Penrose proved that a singularity will form somewhere inside it. Shortly afterwards, Stephen Hawking showed that many cosmological solutions describing the big bang have singularities, in the absence of scalar fields or other exotic matter (see Penrose-Hawking singularity theorems). The Kerr solution, the no-hair theorem and the laws of black hole thermodynamics showed that the physical properties of black holes were simple and comprehensible, making them respectable subjects for research. 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, or because a star which would have been stable receives a lot of extra matter in a way which does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight (the ideal gas law explains the connection between pressure, temperature, and volume).

The collapse may be stopped by the degeneracy pressure of the star's constituents, condensing the matter in an exotic denser state. The result is one of the various types of compact star. Which type of compact star is formed depends on the mass of the remnant - the matter left over after changes triggered by the collapse (such as supernova or pulsations leading to a planetary nebula) have blown away the outer layers. Note that this can be substantially less than the original star - remnants exceeding 5 solar masses are produced by stars which were over 20 solar masses before the collapse.

If the mass of the remnant exceeds ~3-4 solar masses (the Tolman-Oppenheimer-Volkoff limit)—either because the original star was very heavy or because the remnant collected additional mass through accretion of matter)—even the degeneracy pressure of neutrons is insufficient to stop the collapse. After this no known mechanism (except maybe the quark degeneracy pressure, see quark star) is powerful enough to stop the collapse and the object will inevitably collapse to a black hole.

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

Creation of 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. 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. Since classically black holes can take any mass, one would expect micro black holes to be created in any such process no matter how low the energy. 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. 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), where quantum effects are expected to make the theory of general relativity break down completely. This would put the creation of black holes firmly out of reach of any high energy process occurring on or near the Earth. Certain developments in quantum gravity however suggest that this bound could be much lower. Some braneworld scenarios for example put the Planck mass much lower, may be even as low as 1 TeV. This would make it possible for micro black holes to be created in the high energy collisions occurring when cosmic rays hit the Earth's atmosphere, or even maybe in the new Large Hadron Collider at CERN. These theories are however very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists.

Growth

Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb interstellar dust from its direct surroundings and omnipresent cosmic background radiation, but neither of these processes should significantly affect the mass of a stellar black hole. More significant contributions can occur when the black hole formed in a binary star system. After formation the black hole can then leech significant amounts of matter from its companion.

Much larger contributions can be obtained when a black hole merges with other stars or compact objects. The supermassive black holes suspected in the center of most galaxies are expected to have formed from the coagulation of many smaller objects. The process has also been proposed as the origin of some intermediate-mass black holes.

Evaporation

Main article: Hawking radiation

In 1974, Stephen Hawking showed that black holes are not entirely black but emit small amounts of thermal radiation.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.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). 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 in turn is inversely proportional to the mass. Large black holes, therefore, emit less radiation than small black holes.

A stellar black hole of 5 solar masses has a Hawking temperature of about 12 nanokelvins. This is far less than the 2.7 K produced by the cosmic microwave background. Stellar mass (and larger) black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and will thus grow instead of shrink. In order to have a Hawking temperature larger than 2.7 K (and be able to evaporate) a black hole needs to be lighter than the Moon (and therefore a diameter of less than a tenth of a millimeter).

On the other hand if a black hole is very small, the radiation effects are expected to become very strong. Even a black hole that is heavy compared to a human would evaporate in an instant. A black hole the weight of a car (~10^-24 m) would only take a nanosecond to evaporate, during which time it would briefly have a luminosity more than 200 times that of the sun. Lighter black holes are expected to evaporate even faster, for example a black hole of mass 1 TeV/c² would take less than 10^-88 seconds to evaporate completely. Of course, for such a small black hole quantum gravitation effects are expected to play an important role and could even– although current developments in quantum gravity do not indicate so– hypothetically make such a small black hole stable

Observation

Accretion disks and gas jets

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

Most accretion disks and gas jets are not clear proof that a stellar-mass black hole is present, because other massive, ultra-dense objects such as neutron stars and white dwarfs cause accretion disks and gas jets to form and to behave in the same ways as those around black holes. But they can often help by telling astronomers where it might be worth looking for a black hole.

On the other hand, extremely large accretion disks and gas jets may be good evidence for the presence of supermassive black holes, because as far as we know any mass large enough to power these phenomena must be a black hole.

Strong radiation emissions

Steady X-ray and gamma ray emissions also do not prove that a black hole is present, but can tell astronomers where it might be worth looking for one - and they have the advantage that they pass fairly easily through nebulae and gas clouds.

But strong, irregular emissions of X-rays, gamma rays and other electromagnetic radiation can help to prove that a massive, ultra-dense object is not a black hole, so that "black hole hunters" can move on to some other object. Neutron stars and other very dense stars have surfaces, and matter colliding with the surface at a high percentage of the speed of light will produce intense flares of radiation at irregular intervals. Black holes have no material surface, so the absence of irregular flares around a massive, ultra-dense object suggests that there is a good chance of finding a black hole there.

Intense but one-time gamma ray bursts (GRBs) may signal the birth of "new" black holes, because astrophysicists think that GRBs are caused either by the gravitational collapse of giant stars or by collisions between neutron stars, and both types of event involve sufficient mass and pressure to produce black holes. But it appears that a collision between a neutron star and a black hole can also cause a GRB, so a GRB is not proof that a "new" black hole has been formed. All known GRBs come from outside our own galaxy, and most come from billions of light years away so the black holes associated with them are actually billions of years old.

Some astrophysicists believe that some ultraluminous X-ray sources may be the accretion disks of intermediate-mass black holes.

Quasars are thought to be the accretion disks of supermassive black holes, since no other known object is powerful enough to produce such strong emissions. Quasars produce strong emission across the electromagnetic spectrum, including UV, X-rays and gamma-rays and are visible at tremendous distances due to their high luminosity. Between 5 and 25% of quasars are "radio loud," so called because of their powerful radio emission.

Gravitational lensing

A gravitational lens is formed when the light from a very distant, bright source (such as a quasar) is "bent" around a massive object (such as a black hole) between the source object and the observer. The process is known as gravitational lensing, and is one of the predictions of the general theory of relativity. According to this theory, mass "warps" space-time to create gravitational fields and therefore bend light as a result.

A source image behind the lens may appear as multiple images to the observer. In cases where the source, massive lensing object, and the observer lie in a straight line, the source will appear as a ring behind the massive object.

Gravitational lensing can be caused by objects other than black holes, because any very strong gravitational field will bend light rays. Some of these multiple-image effects are probably produced by distant galaxies.

Orbiting objects

See also: Kepler problem in general relativity

A Chandra X-ray spectrum of Cygnus X-1 showing a characteristic peak near 6.4 keV due to ionized iron in the accretion disk, but the peak is gravitationally red-shifted, broadened by the Doppler effect, and skewed toward lower energies.

Objects orbiting black holes probe the gravitational field around the central object. An early example, discovered in the 1970s, is the accretion disk orbiting the putative black hole responsible for Cygnus X-1, a famous X-ray source. While the material itself cannot be seen directly, the X rays flicker on a millisecond time scale, as expected for hot clumpy material orbiting a ~10 solar-mass black hole just prior to accretion. The X-ray spectrum exhibits the characteristic shape expected for a disk of orbiting relativistic material, with an iron line, emitted at ~6.4 keV, broadened to the red (on the receding side of the disk) and to the blue (on the approaching side).

Another example is the star S2, seen orbiting the Galactic center. Here the star is several light hours from the ~3.5×10⁶ solar mass black hole, so its orbital motion can be plotted. Nothing is observed at the center of the observed orbit, the position of the black hole itself—as expected for a black object.

Determining the mass of black holes

Quasi-periodic oscillations can be used to determine the mass of black holes. The technique uses a relationship between black holes and the inner part of their surrounding disks, where gas spirals inward before reaching the event horizon. As the gas collapses inwards, it radiates X-rays with an intensity that varies in a pattern that repeats itself over a nearly regular interval. This signal is the Quasi-Periodic Oscillation, or QPO. A QPO’s frequency depends on the black hole’s mass; the event horizon lies close in for small black holes, so the QPO has a higher frequency. For black holes with a larger mass, the event horizon is farther out, so the QPO frequency is lower.

Black hole candidates

Supermassive

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.

According to the American Astronomical Society, every large galaxy has a supermassive black hole at its center. The black hole’s mass is proportional to the mass of the host galaxy, suggesting that the two are linked very closely. The Hubble Space Telescope and ground-based telescopes in Hawaii were used in a large survey of galaxies.

For decades, astronomers have used the term "active galaxy" to describe galaxies with unusual characteristics, such as unusual spectral line emission and very strong radio emission. However, theoretical and observational studies have shown that the active galactic nuclei (AGN) in these galaxies may contain supermassive black holes. The models of these AGN consist of a central black hole that may be millions or billions of times more massive than the Sun; a disk of gas and dust called an accretion disk; and two jets that are perpendicular to the accretion disk.

Although supermassive black holes are expected to be found in most AGN, only some galaxies' nuclei have been more carefully studied in attempts to both identify and measure the actual masses of the central supermassive black hole candidates. Some of the most notable galaxies with supermassive black hole candidates include the Andromeda Galaxy, M32, M87, NGC 3115, NGC 3377, NGC 4258, and the Sombrero Galaxy.

Astronomers are confident that our own Milky Way galaxy has a supermassive black hole at its center, in a region called Sagittarius A*:

• A star called S2 (star) follows an elliptical orbit with a period of 15.2 years and a pericenter (closest) distance of 17 light hours from the central object.
• The first estimates indicated that the central object contains 2.6 million solar masses and has a radius of less than 17 light hours. Only a black hole can contain such a vast mass in such a small volume.
• Further observations strengthened the case for a black hole, by showing that the central object's mass is about 3.7 million solar masses and its radius no more than 6.25 light-hours.

Intermediate-mass

In 2002, the Hubble Space Telescope produced observations indicating that globular clusters named M15 and G1 may contain intermediate-mass black holes. This interpretation is based on the sizes and periods of the orbits of the stars in the globular clusters. But the Hubble evidence is not conclusive, since a group of neutron stars could cause similar observations. Until recent discoveries, many astronomers thought that the complex gravitational interactions in globular clusters would eject newly-formed black holes.

In November 2004 a team of astronomers reported the discovery of the first well-confirmed intermediate-mass black hole in our Galaxy, orbiting three light-years from Sagittarius A*. This black hole of 1,300 solar masses is within a cluster of seven stars, possibly the remnant of a massive star cluster that has been stripped down by the Galactic Centre. This observation may add support to the idea that supermassive black holes grow by absorbing nearby smaller black holes and stars.

In January 2007, researchers at the University of Southampton in the United Kingdom reported finding a black hole, possibly of about 10 solar masses, in a globular cluster associated with a galaxy named NGC 4472, some 55 million light-years away.

Stellar-mass

Artist's impression of a binary system consisting of a black hole and a main sequence star. The black hole is drawing matter from the main sequence star via an accretion disk around it, and some of this matter forms a gas jet.

Our Milky Way galaxy contains several probable stellar-mass black holes which are closer to us than the supermassive black hole in the Sagittarius A* region. These candidates are all members of X-ray binary systems in which the denser object draws matter from its partner via an accretion disk. The probable black holes in these pairs range from three to more than a dozen solar masses. The most distant stellar-mass black hole ever observed is a member of a binary system located in the Messier 33 galaxy.

Micro

There is theoretically no smallest size for a black hole. Once created, it has the properties of a black hole. Stephen Hawking theorized that primordial black holes could evaporate and become even tinier, i.e. micro black holes. Searches for evaporating primordial black holes are proposed for the Fermi Gamma-ray Space Telescope, which was launched on June 11, 2008. However, if micro black holes can be created by other means, such as by cosmic ray impacts or in colliders, that does not imply that they must evaporate.

The formation of black hole analogs on Earth in particle accelerators has been reported. These black hole analogs are not the same as gravitational black holes, but they are vital testing grounds for quantum theories of gravity.

They act like black holes because of the correspondence between the theory of the strong nuclear force, which has nothing to do with gravity, and the quantum theory of gravity. They are similar because both are described by string theory. So the formation and disintegration of a fireball in quark gluon plasma can be interpreted in black hole language. The fireball at the Relativistic Heavy Ion Collider [RHIC] is a phenomenon which is closely analogous to a black hole, and many of its physical properties can be correctly predicted using this analogy. The fireball, however, is not a gravitational object. It is presently unknown whether the much more energetic Large Hadron Collider [LHC] would be capable of producing the speculative large extra dimension micro black hole, as many theorists have suggested. See Safety of particle collisions at the Large Hadron Collider for a more in depth discussion.

Advanced Topics

Worm Holes

Main article: Wormholes

Diagram of a Schwarzschild wormhole.

General relativity describes the possibility of configurations in which two black holes are connected to each other. Such a configuration is usually called a wormhole. Wormholes have inspired science fiction authors because they offer a means to travel quickly over long distances and even time travel. In practice, such configurations, seem completely unfeasible in astrophysics, because no known process seems to allow the formation of such objects.

Holographic world

Leonard Susskind and Nobel prizewinner Gerard 't Hooft have suggested that a black hole is a two dimensional object extant in three dimensional space. In addition, they believe these results may indicate a solution to the black hole information-loss paradox and that we live in a holographic world.

Entropy and Hawking radiation

In 1971, Stephen Hawking showed that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and swallow each other; that is merge. This is remarkably similar to the Second Law of Thermodynamics, with area playing the role of entropy. As a classical object with zero temperature it was assumed that black holes had zero entropy; if so the second law of thermodynamics would be violated by an entropy-laden material entering the black hole, resulting in a decrease of the total entropy of the universe. Therefore, Jacob Bekenstein proposed that a black hole should have an entropy, and that it should be proportional to its horizon area. Since black holes do not classically emit radiation, the thermodynamic viewpoint seemed simply an analogy, since zero temperature implies infinite changes in entropy with any addition of heat, which implies infinite entropy. However, in 1974, Hawking applied quantum field theory to the curved spacetime around the event horizon and discovered that black holes emit Hawking radiation, a form of thermal radiation, allied to the Unruh effect, which implied they had a positive temperature. This strengthened the analogy being drawn between black hole dynamics and thermodynamics: using the first law of black hole mechanics, it follows that the entropy of a non-rotating black hole is one quarter of the area of the horizon. This is a universal result and can be extended to apply to cosmological horizons such as in de Sitter space. It was later suggested that black holes are maximum-entropy objects, meaning that the maximum possible entropy of a region of space is the entropy of the largest black hole that can fit into it. This led to the holographic principle.

The Hawking radiation reflects a characteristic temperature of the black hole, which can be calculated from its entropy. The more its temperature falls, the more massive a black hole becomes: the more energy a black hole absorbs, the colder it gets. A black hole with roughly the mass of the planet Mercury would have a temperature in equilibrium with the cosmic microwave background radiation (about 2.73 K). More massive than this, a black hole will be colder than the background radiation, and it will gain energy from the background faster than it gives energy up through Hawking radiation, becoming even colder still. However, for a less massive black hole the effect implies that the mass of the black hole will slowly evaporate with time, with the black hole becoming hotter and hotter as it does so. Although these effects are negligible for black holes massive enough to have been formed astronomically, they would rapidly become significant for hypothetical smaller black holes, where quantum-mechanical effects dominate. Indeed, small black holes are predicted to undergo runaway evaporation and eventually vanish in a burst of radiation.

File:First Gold Beam-Beam Collision Events at RHIC at 100 100 GeV c per beam recorded by STAR.jpg

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.

Although general relativity can be used to perform a semi-classical calculation of black hole entropy, this situation is theoretically unsatisfying. In statistical mechanics, entropy is understood as counting the number of microscopic configurations of a system which have the same macroscopic qualities(such as mass, charge, pressure, etc.). But without a satisfactory theory of quantum gravity, one cannot perform such a computation for black holes. Some promise has been shown by string theory, however. There one posits that the microscopic degrees of freedom of the black hole are D-branes. By counting the states of D-branes with given charges and energy, the entropy for certain supersymmetric black holes has been reproduced. Extending the region of validity of these calculations is an ongoing area of research.

Black 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. That is, if the position and velocity of every particle in the universe were measured, we could (disregarding chaos) work backwards to discover the history of the universe arbitrarily far in the past. In quantum mechanics, this corresponds to a vital property called unitarity, which has to do with the conservation of probability.

Black holes, however, might violate this rule. The position under classical general relativity is subtle but straightforward: because of the classical no hair theorem, we can never determine what went into the black hole. However, as seen from the outside, information is never actually destroyed, as matter falling into the black hole takes an infinite time to reach the event horizon.

Ideas about quantum gravity, on the other hand, suggest that there can only be a limited finite entropy (i.e. a maximum finite amount of information) associated with the space near the horizon; but the change in the entropy of the horizon plus the entropy of the Hawking radiation is always sufficient to take up all of the entropy of matter and energy falling into the black hole.

Many physicists are concerned however that this is still not sufficiently well understood. In particular, at a quantum level, is the quantum state of the Hawking radiation uniquely determined by the history of what has fallen into the black hole; and is the history of what has fallen into the black hole uniquely determined by the quantum state of the black hole and the radiation? This is what determinism, and unitarity, would require.

For a long time Stephen Hawking had opposed such ideas, holding to his original 1975 position that the Hawking radiation is entirely thermal and therefore entirely random, containing none of the information held in material the hole has swallowed in the past; this information he reasoned had been lost. However, on 21 July 2004 he presented a new argument, reversing his previous position. On this new calculation, the entropy (and hence information) associated with the black hole escapes in the Hawking radiation itself. However, making sense of it, even in principle, is difficult until the black hole completes its evaporation. Until then it is impossible to relate in a 1:1 way the information in the Hawking radiation (embodied in its detailed internal correlations) to the initial state of the system. Once the black hole evaporates completely, such identification can be made, and unitarity is preserved.

By the time Hawking completed his calculation, it was already very clear from the AdS/CFT correspondence that black holes decay in a unitary way. This is because the fireballs in gauge theories, which are analogous to Hawking radiation, are unquestionably unitary. Hawking's new calculation has not been evaluated by the specialist scientific community, because the methods he uses are unfamiliar and of dubious consistency; but Hawking himself found it sufficiently convincing to pay out on a bet he had made in 1997 with Caltech physicist John Preskill, to considerable media interest.

Further reading

Popular reading

• 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 {{citation}}: Check |isbn= value: checksum (help).
• 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.
• Thorne, Kip S. (1994), Black Holes and Time Warps, Norton, W. W. & Company, Inc, ISBN 0-393-31276-3.
• Stern, B. (2008), Blackhole, poem.

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. (eds.), 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. arXiv: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. (2005). "Stellar Orbits around the Galactic Center Black Hole". The Astrophysical Journal. 620: 744. doi:10.1086/427175. arXiv: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". arXiv:hep-ph/0511217v2. {{cite arXiv}}: |class= ignored (help) Lecture notes from 2005 SLAC Summer Institute.

External links

• Black Hole confirmed in Milky Wayretrieved Dec 10, 2008
• Yale University Video Lecture: Introduction to Black Holes at Google Video
• Black Holes: Gravity's Relentless Pull - Award-winning interactive multimedia Web site about the physics and astronomy of black holes from the Space Telescope Science Institute
• FAQ on black holes
• Schwarzschild Geometry on Andrew Hamilton’s website
• Tufts University: Student Project (Great Kid's Section)
• Movie of Black Hole Candidate from Max Planck Institute
• UT Brownsville Group Simulates Spinning Black-Hole Binaries
• Black Hole Research News on ScienceDaily
• Scientific American Magazine (July 2003 Issue) The Galactic Odd Couple - giant black holes and stellar baby booms
• Scientific American Magazine (May 2005 Issue) Quantum Black Holes
• SPACE.com All About Black Holes - News, Features and Interesting Original Videos
• Black Holes Intro - Introduction to Black Holes
• Advanced Mathematics of Black Hole Evaporation
• HowStuffWorks: How Black Holes Work - Easy to consume guide to Black Holes
• Ted Bunn's Black Holes FAQ explains in simple language some other consequences of the way in which black holes bend space-time.
• Is the Mass of Black Holes Limited? - The Future of Things article