black hole

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black hole,

in astronomy, celestial object of such extremely intense gravity that it attracts everything near it and in some instances prevents everything, including light, from escaping. The term was first used in reference to a star in the last phases of gravitational collapse (the final stage in the life history of certain stars; see stellar evolutionstellar evolution,
life history of a star, beginning with its condensation out of the interstellar gas (see interstellar matter) and ending, sometimes catastrophically, when the star has exhausted its nuclear fuel or can no longer adjust itself to a stable configuration.
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) by the American physicist John A. WheelerWheeler, John Archibald,
1911–2008, American physicist and educator, b. Jacksonville, Fla. Educated at Johns Hopkins (Ph.D., 1933), he joined the faculty at Princeton in 1938, and after 1976 was director of the Center for Theoretical Physics at the Univ.
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Gravitational collapse begins when a star has depleted its steady sources of nuclear energy and can no longer produce the expansive force, a result of normal gas pressurepressure,
in mechanics, ratio of the force acting on a surface to the area of the surface; it is thus distinct from the total force acting on a surface. A force can be applied to and sustained by a single point on a solid.
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, that supports the star against the compressive force of its own gravitationgravitation,
the attractive force existing between any two particles of matter. The Law of Universal Gravitation

Since the gravitational force is experienced by all matter in the universe, from the largest galaxies down to the smallest particles, it is often called
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. As the star shrinks in size (and increases in density), it may assume one of several forms depending upon its mass. A less massive star may become a white dwarfwhite dwarf,
in astronomy, a type of star that is abnormally faint for its white-hot temperature (see mass-luminosity relation). Typically, a white dwarf star has the mass of the sun and the radius of the earth but does not emit enough light or other radiation to be easily
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, while a more massive one would become a supernovasupernova,
a massive star in the latter stages of stellar evolution that suddenly contracts and then explodes, increasing its energy output as much as a billionfold. Supernovas are the principal distributors of heavy elements throughout the universe; all elements heavier than
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. If the mass is less than three times that of the sun, it will then form a neutron starneutron star,
extremely small, extremely dense star, with as much as double the sun's mass but only a few miles in radius, in the final stage of stellar evolution. Astronomers Baade and Zwicky predicted the existence of neutron stars in 1933.
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. However, if the final mass of the remaining stellar core is more than three solar masses, as shown by the American physicists J. Robert OppenheimerOppenheimer, J. Robert
, 1904–67, American physicist, b. New York City, grad. Harvard (B.A., 1925), Ph.D. Univ. of Göttingen, 1927. He taught at the Univ. of California and the California Institute of Technology from 1929 (as professor from 1936) until his appointment
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 and Hartland S. Snyder in 1939, nothing remains to prevent the star from collapsing without limit to an indefinitely small size and infinitely large density, a point called the "singularity."

At the point of singularity the effects of Einstein's general theory of relativityrelativity,
physical theory, introduced by Albert Einstein, that discards the concept of absolute motion and instead treats only relative motion between two systems or frames of reference.
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 become paramount. According to this theory, space becomes curved in the vicinity of matter; the greater the concentration of matter, the greater the curvature. When the star (or supernova remnant) shrinks below a certain size determined by its mass, the extreme curvature of space seals off contact with the outside world. The place beyond which no radiation can escape is called the event horizon, and its radius is called the Schwarzschild radius after the German astronomer Karl Schwarzschild, who in 1916 postulated the existence of collapsed celestial objects that emit no radiation. For a star with a mass equal to that of the sun, this limit is a radius of only 1.86 mi (3.0 km). Even light cannot escape a black hole, but is turned back by the enormous pull of gravitation.

It is now believed that the origin of some black holes is nonstellar. Some astrophysicists suggest that immense volumes of interstellar matterinterstellar matter,
matter in a galaxy between the stars, known also as the interstellar medium. Distribution of Interstellar Matter

Compared to the size of an entire galaxy, stars are virtually points, so that the region occupied by the interstellar matter
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 can collect and collapse into supermassive black holes, such as are found at the center of large galaxies. The British physicist Stephen HawkingHawking, Stephen William,
1942–, British theoretical physicist, b. Oxford, England, grad. University College, Oxford, 1962, Ph.D. Trinity Hall, Cambridge, 1966. In 1962 Hawking was diagnosed as having an incurable muscular disease, amyotrophic lateral sclerosis (ALS).
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 has postulated still another kind of nonstellar black hole. Called a primordial, or mini, black hole, it would have been created during the "big bang," in which the universe was created (see cosmologycosmology,
area of science that aims at a comprehensive theory of the structure and evolution of the entire physical universe. Modern Cosmological Theories
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). Unlike stellar black holes, primordial black holes create and emit elementary particleselementary particles,
the most basic physical constituents of the universe. Basic Constituents of Matter

Molecules are built up from the atom, which is the basic unit of any chemical element. The atom in turn is made from the proton, neutron, and electron.
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, called Hawking radiation, until they exhaust their energy and expire. It has also been suggested that the formation of black holes may be associated with intense gamma ray bursts. Beginning with a giant star collapsing on itself or the collision of two neutron stars, waves of radiation and subatomic particles are propelled outward from the nascent black hole and collide with one another, releasing the gamma radiationgamma radiation,
high-energy photons emitted as one of the three types of radiation resulting from natural radioactivity. It is the most energetic form of electromagnetic radiation, with a very short wavelength (high frequency).
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. Also released is longer-lasting electromagnetic radiationelectromagnetic radiation,
energy radiated in the form of a wave as a result of the motion of electric charges. A moving charge gives rise to a magnetic field, and if the motion is changing (accelerated), then the magnetic field varies and in turn produces an electric field.
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 in the form of X raysX ray,
invisible, highly penetrating electromagnetic radiation of much shorter wavelength (higher frequency) than visible light. The wavelength range for X rays is from about 10−8 m to about 10−11
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, radio waves, and visible wavelengths that can be used to pinpoint the location of the disturbance.

Because light and other forms of energy and matter are permanently trapped inside a black hole, it can never be observed directly. However, a black hole can be detected by the effect of its gravitational field on nearby objects (e.g., if it is orbited by a visible star), during the collapse while it was forming, or by the X rays and radio frequency signals emitted by rapidly swirling matter being pulled into the black hole. The first discovery (1971) of a possible black hole was Cygnus X-1, an X-ray source in the constellation Cygnus. In 1994 astronomers employing the Hubble Space TelescopeHubble Space Telescope
(HST), the first large optical orbiting observatory. Built from 1978 to 1990 at a cost of $1.5 billion, the HST (named for astronomer E. P. Hubble) was expected to provide the clearest view yet obtained of the universe from a position some 350 mi (560 km)
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 announced that they had found conclusive evidence of a supermassive black hole in the M87 galaxy in the constellation Virgo. Since then others have been found, and in 2011 astronomers announnced the discovery of one, in NGC 4889 in the constellation Coma, whose mass may be as great as 21 billion times that of the sun. The first evidence (2002) of a binary black hole, two supermassive black holes circling one another, was detected in images from the orbiting Chandra X-ray Observatory. Located in the galaxy NGC6240, the pair are 3,000 light years apart, travel around each other at a speed of about 22,000 mph (35,415 km/hr), and have the mass of 100 million suns each. As the distance between them shrinks over 100 million years, the circling speed will increase until it approaches the speed of light, about 671 million mph (1,080 million km/hr). The black holes will then collide spectacularly, spewing radiation and gravitational waves across the universe. The Chandra observatory has also discovered that massive black holes were associated with galaxies that existed 13 billion years ago. Subsequently, in 2015, the Laser Interferometer Gravitational Wave Observatory detected gravitational waves that resulted from the merging of two other pairs of black holes.


See S. W. Hawking, Black Holes and Baby Universes and Other Essays (1994); P. Strathern, The Big Idea: Hawking and Black Holes (1998); J. A. Wheeler, Geons, Black Holes, and Quantum Foam: A Life in Physics (1998); H. Falcke and F. W. Hehl, The Galactic Black Hole: Studies in High Energy Physics, Cosmology and Gravitation (2002); M. Bartusiak, Black Hole (2015).

black hole

An object so collapsed that its escape velocity exceeds the speed of light. It becomes a black hole when its radius has shrunk to its Schwarzschild radius and light can no longer escape. Although gravity will make the object shrink beyond this limit, the ‘surface’ having this critical value of radius – the event horizon – marks the boundary inside which all information is trapped. Calculations, however, indicate that space and time (see spacetime) become highly distorted inside the event horizon, and that the collapsing object's ultimate fate is to be compressed to an infinitely dense singularity at the center of the black hole. It has also been shown that the distortion of spacetime just outside the Schwarzschild radius causes the production of particles and radiation that gradually rob the black hole of energy and thus slowly diminish its mass. This Hawking radiation (Stephen Hawking, 1974) depends inversely on the black hole's mass, so the most massive black holes ‘evaporate’ most slowly. A black hole of the Sun's mass would last 1066 years.

Once matter (or antimatter) has disappeared into a black hole, only three of its original properties can be ascertained: the total mass, the net electric charge, and the total angular momentum. Because all black holes must have mass, there are four possible types of black hole: a Schwarzschild black hole (1916) has no charge and no angular momentum; a Reissner–Nordstrom black hole (1918) has charge but no angular momentum; a Kerr black hole (1963) has angular momentum but no charge; a Kerr-Newman black hole (1965) has charge and angular momentum. (The dates in brackets indicate when the named mathematician(s) solved the equations of general relativity for these particular cases.) In astrophysics the simple Schwarzschild solution is often used, but real black holes are almost certainly rotating and have very little electric charge, so that the Kerr solution should be the most applicable.

The most promising candidates for black holes are massive stars that explode as supernovae, leaving a core in excess of 3 solar masses. This core must undergo complete gravitational collapse because it is above the stable limit for both white dwarfs and neutron stars. Once formed, a black hole can be detected only by its gravity. Finding black holes only a few kilometers across (the size of the event horizon for a single-star black hole) is exceedingly difficult, but chances are increased if the black hole is a member of a close binary system. If the components of a binary system are close enough, mass transfer can occur between the primary star and its more compact companion (see equipotential surfaces). Matter will not fall directly on to the companion, however, for it has too much angular momentum; instead it forms a rapidly spinning disk – an accretion disk – around the compact object. If the latter is a black hole considerable energy can be produced, predominantly at X-ray wavelengths, as matter in the accretion disk loses angular momentum and spirals in. When the accreting matter is unable to cool efficiently, most of the energy generated in the disk due to viscosity is not radiated away, but instead stored in the gas as internal energy and advected inward in an advection-dominated accretion flow onto the central object.

Candidates for black holes in a binary system fall into two classes, massive and low-mass black-hole binaries, depending on the mass of the companion star. The first massive black-hole candidate to be identified was the X-ray binary Cygnus X-1, comprising a 20 solar mass B0 supergiant accompanied by an invisible companion with a mass about 10 times that of the Sun. This massive nonluminous object is probably a black hole emitting X-rays from its accretion disk. Another promising massive black-hole candidate is the X-ray binary LMC X-3 in the Large Magellanic Cloud. While the probable mass of the compact objects in this system is of the order of 10 solar masses, rigorous lower limits are as low as 3 solar masses (possibly even lower), marginally consistent with the maximum theoretically predicted mass of a neutron star. Even better evidence for a stellar-mass black hole comes from some of the low-mass black-hole candidates, in particular A0620-00 in Monoceros and V404 Cygni. Rigorous limits on the masses of the compact objects in A0620-00 and V404 Cygni are 3 and 6 solar masses, respectively. See also gamma-ray transients.

Supermassive black holes of 106 to 109 solar masses probably lie in the centers of some galaxies and give rise to the quasar phenomenon and the phenomena of other active galaxies. If a huge black hole is able to form and to capture sufficient gas and/or stars from its surroundings, the rest-mass energy of infalling material can be converted into radiation or energetic particles. There is now observational evidence to support this hypothesis. the dynamical motion of stars and ionized gas in the cores of nearby galaxies show that they are responding to a strong gravitational field, in excess of that expected from the number of stars accounting for the light at the galaxy center. These motions are thought to be due to the presence of the supermassive black hole (see Seyfert galaxy; Virgo A). Other strong evidence for the presence of supermassive black holes is found from recent observations of an extremely broad iron fluorescence line in the X-rays from several Seyfert galaxies; this line has a very particular shape, revealing its origin in an accretion disk very close to the central black hole.

At the other mass extreme are the more speculative mini black holes, weighing only 1011 kg and with radii of 10–10 meters. These could have formed in the highly turbulent conditions existing after the Big Bang. They create such intense localized gravitational fields that their Hawking radiation makes them explode within the lifetime of the Universe; their final burst of gamma rays and microwaves should be detectable but has not yet been found.

Black Hole


a celestial object that is formed as a result of the relativistic gravitational collapse of a massive body. In particular, the evolution of a star whose mass at the moment of collapse exceeds some critical value may terminate in catastrophic gravitational collapse. The value of the critical mass is not precisely determined and, depending on the equation of state of matter used, ranges from 1.5 to 3 solar masses (Mʘ).

For any equation of state of matter, the general theory of relativity predicts that no stable equilibrium exists for cold stars of several solar masses. If, after a star becomes unstable, not enough energy is released to halt the collapse or to cause a partial explosion after which the remaining mass would be less than the critical mass, the central portions of the star collapse and, in a short time, reach the gravitational radius rg. No forces whatsoever can prevent the further collapse of a star if the radius of the star shrinks down to rg, which is also known as the Schwarzschild radius and is the radius of a sphere whose surface is called the event horizon. A fundamental property of the event horizon is that no signals emitted from the surface of the star and reaching the event horizon can escape from the region inside that horizon. Thus, as a result of the gravitational collapse of a massive star, a region in space-time is formed from which no information whatsoever about physical processes occurring within the region can emerge.

A black hole has a gravitational field whose properties are determined by the hole’s mass, angular momentum, and—if the collapsing star was electrically charged—electric charge. At large distances, the gravitational field of a black hole is virtually indistinguishable from the gravitational field of a normal star. In addition, the motion of other objects that interact with a black hole at large distances is governed by the laws of Newtonian mechanics. Calculations show that a region known as the ergosphere, which is bounded by a surface called the static, or stationary, limit, should exist outside the event horizon of a rotating black hole. The attractive force that a black hole exerts on a stationary object situated in the ergosphere tends to infinity. However, the attractive force is finite if the object has an angular momentum whose direction coincides with that of the black hole’s angular momentum. Therefore, any particles that happen to be in the ergosphere will revolve around the black hole.

The presence of an ergosphere may lead to energy losses by a rotating black hole. In particular, energy losses are possible in the case where some object that has entered the ergosphere breaks up (for example, as a result of an explosion) into two fragments near the event horizon of the black hole. In this case, one of the fragments continues to fall into the black hole, but the other fragment escapes from the ergosphere. The parameters of the explosion may be such that the energy of the fragment that escapes from the ergosphere is higher than the energy of the original object. The additional energy in this case is drawn from the rotational energy of the black hole.

As the angular momentum of a rotating black hole decreases, the static limit comes closer to the event horizon; when the angular momentum is zero, the static limit and the event horizon coincide and the ergosphere disappears. Owing to the effects of the centrifugal force of rotation, the rapid rotation of a collapsing object prevents the formation of a black hole. Therefore, a black hole cannot have an angular momentum that is greater than some extreme value.

Quantum-mechanical calculations show that particles—such as photons, neutrinos, gravitons, and electron-positron pairs—may be produced in the strong gravitational field of a black hole. As a result, a black hole radiates like a blackbody with an effective temperature of T = 10–6 (Mʘ/M) °K, where M is the mass of the black hole, even in cases where no matter whatsoever falls into the hole. The energy of the radiation is drawn from the energy of the black hole’s gravitational field; as a result, the mass of the black hole decreases with time. However, owing to their low efficiency, the quantum radiation processes are unimportant for massive black holes, which are formed as a result of stellar collapse.

In the early stages of the evolution of the universe, which were hot and ultradense, black holes with masses ranging from 10–5 g to a solar mass or higher may have been formed as a result of an inhomogeneous distribution of matter. In contrast to the black holes that are formed by collapsed stars, these objects are called primordial black holes. Since quantum radiation processes reduce the mass of a black hole, all primordial black holes with a mass of less than 1015 g should have evaporated by the present time. The intensity and effective temperature of black-hole radiation increase as the mass of a black hole decreases. Therefore, in the final stage, the evaporation of a black hole with a mass of the order of 3 × 109 g would be an explosion accompanied by an energy release of 1030 erg in 0.1 sec. Primordial black holes with a mass of greater than 1015 g have remained virtually unchanged. The detection of primordial black holes on the basis of their radiation would make it possible to draw important conclusions about the physical processes that occurred in the early stages of the evolution of the universe.

The search for black holes in the universe is a task of current interest in modern astronomy. Searches are carried out on the assumption that black holes may be the invisible components of certain binary star systems. However, this inference is not definite, since the normal star in a binary system may be invisible against the higher luminosity of the second component. Another method of identifying black holes in binary systems is based on the radiation emitted by matter flowing from the companion, which is a normal star, to the black hole. In this case, a disk consisting of matter flowing to the black hole is formed near the hole; the layers of the disk move around the hole with various velocities (see Figure 1). Owing to friction between adjacent layers, the matter in the disk is heated to tens of millions of degrees. The inner regions of the disk emit energy in the X-ray region of the electromagnetic spectrum. The same type of radiation is produced in the case where a binary system contains a neutron star rather than a black hole. However, a neutron star cannot have a mass higher than some limiting value.

As a result of space studies, a large number of X-ray sources in binary systems have been discovered. The X-ray source Cygnus X-l is the most likely candidate for a black hole. In this binary system, the mass of the X-ray source, which may be estimated from the observed orbital velocity of the optical star and from Kepler’s laws, exceeds 5 Mʘ, that is, is higher than the limiting mass for a neutron star.

Figure 1. A black hole in a binary star system

The hypothesis has also been advanced that supermassive black holes—that is, black holes with a mass M ≃ 106–108Mʘ—may be located in the nuclei of active galaxies and in quasars. In this case, the activity of the active galactic nuclei and quasars is attributed to the infall of ambient gas onto the black hole.


Zel’dovich, Ia. B., and I. D. Novikov. Teoriia tiagoteniia i evoliutsiia zvezd. Moscow, 1971.
Penrose, R. “Chernydyry.” Uspekhi fizicheskik nauk, 1973, vol. 109, issue 2.
Shklovskii, I. S. Zvezdy: Ikh rozhdenie, zhizn’ i smert’. Moscow, 1975.
Thorne, K. “Poiski chernykh dyr.” Uspekhi fizicheskikh nauk, 1976, vol. 118, issue 3. (Article translated from English.)
Frolov, V. P. “Chernye dyry i kvantovye protsessy v nikh.” Uspekhi fizicheskik nauk, 1976, vol. 118, issue 3.
Shakura, N. I. Neitronnye zvezdy i “chernye dyry” v dvoinykh zvezdnykh sistemakh. Moscow, 1976.
Novikov, I. D. Chernye dyry vo Vselennoi. Moscow, 1977.
Misner, C, K. Thorne, and J. Wheeler. Gravitatsiia, vols. 1–3. Moscow, 1977. (Translated from English.)


black hole

[¦blak ′hōl]
(computer science)
A region of space-time from which nothing can escape, according to classical physics; quantum corrections indicate a black hole radiates particles with a temperature inversely proportional to the mass and directly proportional to Planck's constant.

black hole

an object in space so dense that its escape velocity exceeds the speed of light

black hole

An expression which depends on its own value or a technique to detect such expressions. In graph reduction, when the reduction of an expression is begun, the root of the expression can be overwritten with a black hole. If the expression depends on its own value, e.g.

x = x + 1

then it will try to evaluate the black hole which will usually print an error message and abort the program. A secondary effect is that, once the root of the expression has been black-holed, parts of the expression which are no longer required may be freed for garbage collection.

Without black holes the usual result of attempting to evaluate an expression which depends on itself would be a stack overflow. If the expression is evaluated successfully then the black hole will be updated with the value.

Expressions such as

ones = 1 : ones

are not black holes because the list constructor, : is lazy so the reference to ones is not evaluated when evaluating ones to WHNF.

black hole

Where an electronic mail message or news aritcle has gone if it disappears mysteriously between its origin and destination sites without returning a bounce message. Compare bit bucket.
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