A
black hole is a region of
spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being threedimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
from which nothing, not even
lightLight or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
, can escape. The theory of
general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
predicts that a sufficiently compact
massMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an
event horizonIn general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...
that marks the point of no return. It is called "black" because it absorbs all the light that hits the horizon, reflecting nothing, just like a perfect
black bodyA black body is an idealized physical body that absorbs all incident electromagnetic radiation. Because of this perfect absorptivity at all wavelengths, a black body is also the best possible emitter of thermal radiation, which it radiates incandescently in a characteristic, continuous spectrum...
in
thermodynamicsThermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
.
Quantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particlelike and wavelike behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
predicts that black holes emit
radiationHawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...
like a black body with a finite
temperatureTemperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
. This temperature is inversely proportional to the mass of the black hole, making it difficult to observe this radiation for
black holes of stellar massA stellar black hole is a black hole formed by the gravitational collapse of a massive star. They have masses ranging from about 3 to several tens of solar masses...
or greater.
Objects whose gravity field is too strong for light to escape were first considered in the 18th century by
John MichellJohn Michell was an English natural philosopher and geologist whose work spanned a wide range of subjects from astronomy to geology, optics, and gravitation. He was both a theorist and an experimenter....
and
PierreSimon LaplacePierreSimon, marquis de Laplace was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He summarized and extended the work of his predecessors in his five volume Mécanique Céleste...
. The first modern solution of general relativity that would characterize a black hole was found by
Karl SchwarzschildKarl Schwarzschild was a German physicist. He is also the father of astrophysicist Martin Schwarzschild.He is best known for providing the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical nonrotating mass, which he accomplished...
in 1916, although its interpretation as a region of space from which nothing can escape was not fully appreciated for another four decades. Long considered a mathematical curiosity, it was during the 1960s that theoretical work showed black holes were a generic prediction of general relativity. The discovery of
neutron starA neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...
s sparked interest in
gravitationally collapsedGravitational collapse is the inward fall of a body due to the influence of its own gravity. In any stable body, this gravitational force is counterbalanced by the internal pressure of the body, in the opposite direction to the force of gravity...
compact objects as a possible astrophysical reality.
Black holes of stellar mass are expected to form when massive stars collapse in a
supernovaA supernova is a stellar explosion that is more energetic than a nova. It is pronounced with the plural supernovae or supernovas. Supernovae are extremely luminous and cause a burst of radiation that often briefly outshines an entire galaxy, before fading from view over several weeks or months...
at the end of their life cycle. After a black hole has formed it can continue to grow by absorbing mass from its surroundings. By absorbing other stars and merging with other black holes,
supermassive black holeA supermassive black hole is the largest type of black hole in a galaxy, in the order of hundreds of thousands to billions of solar masses. Most, and possibly all galaxies, including the Milky Way, are believed to contain supermassive black holes at their centers.Supermassive black holes have...
s of millions of solar masses may be formed.
Despite its invisible interior, the presence of a black hole can be inferred through its interaction with other
matterMatter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
. Astronomers have identified numerous stellar black hole candidates in
binary systemsA binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, comes, or secondary...
, by studying their interaction with their companion stars. There is growing consensus that supermassive black holes exist in the centers of most
galaxiesA galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...
. In particular, there is strong evidence of a black hole of more than 4 million
solar massThe solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...
es at the center of our
Milky WayThe Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim unresolved "milky" glowing band arching across the night sky...
.
History
The idea of a body so massive that even light could not escape was first put forward by
geologistA geologist is a scientist who studies the solid and liquid matter that constitutes the Earth as well as the processes and history that has shaped it. Geologists usually engage in studying geology. Geologists, studying more of an applied science than a theoretical one, must approach Geology using...
John MichellJohn Michell was an English natural philosopher and geologist whose work spanned a wide range of subjects from astronomy to geology, optics, and gravitation. He was both a theorist and an experimenter....
in a letter written to
Henry CavendishHenry Cavendish FRS was a British scientist noted for his discovery of hydrogen or what he called "inflammable air". He described the density of inflammable air, which formed water on combustion, in a 1766 paper "On Factitious Airs". Antoine Lavoisier later reproduced Cavendish's experiment and...
in 1783 of the
Royal SocietyThe Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
:
In 1796, mathematician
PierreSimon LaplacePierreSimon, marquis de Laplace was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He summarized and extended the work of his predecessors in his five volume Mécanique Céleste...
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 it was not understood how a massless wave such as light could be influenced by gravity.
General relativity
In 1915,
Albert EinsteinAlbert Einstein was a Germanborn theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
developed his theory of
general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, having earlier shown that gravity does influence light's motion. Only a few months later,
Karl SchwarzschildKarl Schwarzschild was a German physicist. He is also the father of astrophysicist Martin Schwarzschild.He is best known for providing the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical nonrotating mass, which he accomplished...
found a
solutionIn Einstein's theory of general relativity, the Schwarzschild solution describes the gravitational field outside a spherical, uncharged, nonrotating mass such as a star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or...
to
Einstein field equationsThe Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...
, which describes the
gravitational fieldThe gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...
of a point mass and a spherical mass. A few months after Schwarzschild, Johannes Droste, a student of
Hendrik LorentzHendrik Antoon Lorentz was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect...
, independently gave the same solution for the point mass and wrote more extensively about its properties. This solution had a peculiar behaviour at what is now called the
Schwarzschild radiusThe Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...
, where it became
singularIn mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be wellbehaved in some particular way, such as differentiability...
, meaning that some of the terms in the Einstein equations became infinite. The nature of this surface was not quite understood at the time. In 1924, Arthur Eddington showed that the singularity disappeared after a change of coordinates (see Eddington–Finkelstein coordinates), although it took until 1933 for
Georges LemaîtreMonsignor Georges Henri Joseph Édouard Lemaître was a Belgian priest, astronomer and professor of physics at the Catholic University of Louvain. He was the first person to propose the theory of the expansion of the Universe, widely misattributed to Edwin Hubble...
to realize that this meant the singularity at the Schwarzschild radius was an unphysical coordinate singularity.
In 1931,
Subrahmanyan ChandrasekharSubrahmanyan Chandrasekhar, FRS ) was an Indian origin American astrophysicist who, with William A. Fowler, won the 1983 Nobel Prize for Physics for key discoveries that led to the currently accepted theory on the later evolutionary stages of massive stars...
calculated, using special relativity, that a nonrotating body of electrondegenerate matter above a certain limiting mass (now called the
Chandrasekhar limitWhen a star starts running out of fuel, it usually cools off and collapses into one of three compact forms, depending on its total mass:* a White Dwarf, a big lump of Carbon and Oxygen atoms, almost like one huge molecule...
at 1.4 solar masses) has no stable solutions. His arguments were opposed by many of his contemporaries like Eddington and
Lev LandauLev Davidovich Landau was a prominent Soviet physicist who made fundamental contributions to many areas of theoretical physics...
, who argued that some yet unknown mechanism would stop the collapse. They were partly correct: a
white dwarfA white dwarf, also called a degenerate dwarf, is a small star composed mostly of electrondegenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored...
slightly more massive than the Chandrasekhar limit will collapse into a
neutron starA neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...
, which is itself stable because of the
Pauli exclusion principleThe Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is antisymmetric with respect to exchange of the particles...
. But in 1939,
Robert OppenheimerJulius Robert Oppenheimer was an American theoretical physicist and professor of physics at the University of California, Berkeley. Along with Enrico Fermi, he is often called the "father of the atomic bomb" for his role in the Manhattan Project, the World War II project that developed the first...
and others predicted that neutron stars above approximately three solar masses (the Tolman–Oppenheimer–Volkoff limit) would collapse into black holes for the reasons presented by Chandrasekhar, and concluded that no law of physics was likely to intervene and stop at least some stars from collapsing to black holes.
Oppenheimer and his coauthors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infalling observers. Because of this property, the collapsed stars were called "frozen stars," because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius.
Golden age
In 1958,
David FinkelsteinDavid Ritz Finkelstein is currently an emeritus professor of physics at the Georgia Institute of Technology. Finkelstein obtained his Ph.D. in physics at the Massachusetts Institute of Technology in 1953. From 1964 to 1976, he was professor of physics at Yeshiva University.In 1958 Charles W...
identified the Schwarzschild surface as an
event horizonIn general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...
, "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.
Finkelstein's solutionIn general relativity Eddington–Finkelstein coordinates, named for Arthur Stanley Eddington and David Finkelstein, are a pair of coordinate systems for a Schwarzschild geometry which are adapted to radial null geodesics...
extended the Schwarzschild solution for the future of observers falling into a black hole. A
complete extensionIn general relativity Kruskal–Szekeres coordinates, named for Martin Kruskal and George Szekeres, are a coordinate system for the Schwarzschild geometry for a black hole...
had already been found by
Martin KruskalMartin David Kruskal was an American mathematician and physicist. He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and from nonlinear analysis to asymptotic analysis...
, who was urged to publish it.
These results came at the beginning of the
golden age of general relativityThe golden age of general relativity is the period roughly from 1960 to 1975 during which the study of general relativity, which had previously been regarded as something of a curiosity, entered the mainstream of theoretical physics...
, which was marked by general relativity and black holes becoming mainstream subjects of research. This process was helped by the discovery of
pulsarA pulsar is a highly magnetized, rotating neutron star that emits a beam of electromagnetic radiation. The radiation can only be observed when the beam of emission is pointing towards the Earth. This is called the lighthouse effect and gives rise to the pulsed nature that gives pulsars their name...
s in 1967, which were shown to be rapidly rotating
neutron starA neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...
s by 1969. Until that time, neutron stars, like black holes, were regarded as just theoretical curiosities; but the discovery of pulsars showed their physical relevance and spurred a further interest in all types of compact objects that might be formed by gravitational collapse.
In this period more general black hole solutions were found. In 1963,
Roy KerrRoy Patrick Kerr CNZM is a New Zealand mathematician who is best known for discovering the Kerr vacuum, an exact solution to the Einstein field equation of general relativity...
found
the exact solutionThe Kerr metric describes the geometry of empty spacetime around an uncharged axiallysymmetric blackhole with an event horizon which is topologically a sphere. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly nonlinear, which...
for a
rotating black holeA rotating black hole is a black hole that possesses spin angular momentum.Types of black holes:There are four known, exact, black hole solutions to Einstein's equations, which describe gravity in General Relativity. Two of these rotate...
. Two years later,
Ezra NewmanEzra Ted Newman is an American physicist, known for his many contributions to general relativity theory. He is Professor Emeritus at the University of Pittsburgh...
found the axisymmetric solution for a black hole that is both rotating and
electrically chargedElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
. Through the work of
Werner IsraelWerner Israel, OC, FRSC, FRS is a Canadian physicist.Born in Berlin, Germany and raised in Cape Town, South Africa, he received his B.Sc. in 1951 and his M.Sc. in 1954 from the University of Cape Town. He received his Ph.D...
,
Brandon CarterBrandon Carter, FRS is an Australian theoretical physicist, best known for his work on the properties of black holes and for being the first to name and employ the anthropic principle in its contemporary form. He is a researcher at the Meudon campus of the Laboratoire Univers et Théories, part of...
, and David Robinson the nohair theorem emerged, stating that a stationary black hole solution is completely described by the three parameters of the Kerr–Newman metric;
massMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
,
angular momentumIn physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
, and
electric chargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
.
For a long time, it was suspected that the strange features of the black hole solutions were pathological artifacts from the symmetry conditions imposed, and that the singularities would not appear in generic situations. This view was held in particular by Vladimir Belinsky,
Isaak KhalatnikovIsaak Markovich Khalatnikov is a leading Soviet physicist, well known for his role in developing the BKL conjecture in general relativity.Khalatnikov was born in Dnipropetrovsk and graduated from Dnipropetrovsk State University with a degree in Physics in 1941. He has been a member of the...
, and
Evgeny LifshitzEvgeny Mikhailovich Lifshitz was a leading Soviet physicist of Jewish origin and the brother of physicist Ilya Mikhailovich Lifshitz. Lifshitz is well known in general relativity for coauthoring the BKL conjecture concerning the nature of a generic curvature...
, who tried to prove that no singularities appear in generic solutions. However, in the late sixties
Roger PenroseSir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...
and
Stephen HawkingStephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
used global techniques to prove that singularities are generic.
Work by
James BardeenJames Maxwell Bardeen is an American physicist, well known for his work in general relativity, particularly his role in formulating the laws of black hole mechanics. He also discovered the Bardeen vacuum, an exact solution of the Einstein field equation.Bardeen graduated from Harvard in 1960 and...
,
Jacob BekensteinJacob David Bekenstein is an Israeli theoretical physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation.Biography:...
, Carter, and Hawking in the early 1970s led to the formulation of
black hole thermodynamicsIn physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons...
. These laws describe the behaviour of a black hole in close analogy to the
laws of thermodynamicsThe four laws of thermodynamics summarize its most important facts. They define fundamental physical quantities, such as temperature, energy, and entropy, in order to describe thermodynamic systems. They also describe the transfer of energy as heat and work in thermodynamic processes...
by relating mass to energy, area to
entropyEntropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
, and
surface gravityThe surface gravity, g, of an astronomical or other object is the gravitational acceleration experienced at its surface. The surface gravity may be thought of as the acceleration due to gravity experienced by a hypothetical test particle which is very close to the object's surface and which, in...
to
temperatureTemperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
. The analogy was completed when Hawking, in 1974, showed that
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and manybody systems. It is the natural and quantitative language of particle physics and...
predicts that black holes should radiate like a
black bodyA black body is an idealized physical body that absorbs all incident electromagnetic radiation. Because of this perfect absorptivity at all wavelengths, a black body is also the best possible emitter of thermal radiation, which it radiates incandescently in a characteristic, continuous spectrum...
with a temperature proportional to the
surface gravityThe surface gravity, g, of an astronomical or other object is the gravitational acceleration experienced at its surface. The surface gravity may be thought of as the acceleration due to gravity experienced by a hypothetical test particle which is very close to the object's surface and which, in...
of the black hole.
The term "black hole" was first publicly used by
John WheelerJohn Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...
during a lecture in 1967. Although he is usually credited with coining the phrase, he always insisted that it was suggested to him by somebody else. The first recorded use of the term is in a 1964 letter by Anne Ewing to the
American Association for the Advancement of ScienceThe American Association for the Advancement of Science is an international nonprofit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsibility, and supporting scientific education and science outreach for the...
. After Wheeler's use of the term, it was quickly adopted in general use.
Properties and structure
The nohair theorem states that, once it achieves a stable condition after formation, a black hole has only three independent physical properties:
massMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
,
chargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
, and
angular momentumIn physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
. Any two black holes that share the same values for these properties, or parameters, are indistinguishable according to
classicalIn physics, classical mechanics is one of the two major subfields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
(i.e. non
quantumQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particlelike and wavelike behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
) mechanics.
These properties are special because they are visible from outside a black hole. For example, a charged black hole repels other like charges just like any other charged object. Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of
Gauss's lawIn physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. Gauss's law states that:...
, the ADM mass, far away from the black hole. Likewise, the angular momentum can be measured from far away using frame dragging by the
gravitomagnetic fieldGravitomagnetism , refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. The most common version of GEM is valid only far from isolated sources, and for slowly moving test...
.
When an object falls into a black hole, any
informationIn physics, physical information refers generally to the information that is contained in a physical system. Its usage in quantum mechanics In physics, physical information refers generally to the information that is contained in a physical system. Its usage in quantum mechanics In physics,...
about the shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers. The behavior of the horizon in this situation is a
dissipative systemA dissipative system is a thermodynamically open system which is operating out of, and often far from, thermodynamic equilibrium in an environment with which it exchanges energy and matter....
that is closely analogous to that of a conductive stretchy membrane with friction and
electrical resistanceThe electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
—the
membrane paradigmIn black hole theory, the black hole membrane paradigm is a useful "toy model" method or "engineering approach" for visualising and calculating the effects predicted by quantum mechanics for the exterior physics of black holes, without using quantummechanical principles or calculations...
. This is different from other field theories like electromagnetism, which do not have any friction or resistivity at the microscopic level, because they are
timereversibleT Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...
. Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in. The information that is lost includes every quantity that cannot be measured far away from the black hole horizon, including the total
baryon number,
lepton numberIn particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and nonleptonic particles 0...
, and all the other
nearly conservedIn physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
pseudocharges of particle physics. This behavior is so puzzling that it has been called the black hole information loss paradox.
Physical properties
The simplest black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as
Schwarzschild black holeIn Einstein's theory of general relativity, the Schwarzschild solution describes the gravitational field outside a spherical, uncharged, nonrotating mass such as a star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or...
s after Karl Schwarzschild who discovered this
solutionWhere appropriate, this article will use the abstract index notation.Solutions of the Einstein field equations are spacetimes that result from solving the Einstein field equations of general relativity. Solving the field equations actually gives Lorentz metrics...
in 1916. According to
Birkhoff's theoremIn general relativity, Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the exterior solution must be given by the Schwarzschild metric....
, it is the only
vacuum solutionIn general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stressenergy tensor also vanishes identically, so that no matter or nongravitational fields are present.More generally, a...
that is
spherically symmetricA spherically symmetric spacetime is a spacetime whose isometry group contains a subgroup which is isomorphic to the group SO and the orbits of this group are 2dimensional spheres . The isometries are then interpreted as rotations and a spherically symmetric spacetime is often described as one...
. This means that there is no observable difference between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore only correct near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass.
Solutions describing more general black holes also exist.
Charged black holeA charged black hole is a black hole that possesses electric charge. Since the electromagnetic repulsion in compressing an electrically charged mass is dramatically greater than the gravitational attraction , it is not expected that black holes with a significant electric charge will be formed in...
s are described by the Reissner–Nordström metric, while the
Kerr metricThe Kerr metric describes the geometry of empty spacetime around an uncharged axiallysymmetric blackhole with an event horizon which is topologically a sphere. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly nonlinear, which...
describes a
rotating black holeA rotating black hole is a black hole that possesses spin angular momentum.Types of black holes:There are four known, exact, black hole solutions to Einstein's equations, which describe gravity in General Relativity. Two of these rotate...
. The most general
stationaryIn general relativity, specifically in the Einstein field equations, a spacetime is said to be stationary if it admits a Killing vector that is asymptotically timelike....
black hole solution known is the Kerr–Newman metric, which describes a black hole with 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
Planck unitsIn physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units elegantly simplify...
, the total electric charge
Q and the total angular momentum
J are expected to satisfy
for a black hole of mass
M. Black holes saturating this inequality are called
extremalIn theoretical physics, an extremal black hole is a black hole with the minimal possible mass that can be compatible with a given charge and angular momentum . In other words, this is the smallest possible black hole that can exist while rotating at a given fixed constant speed.The concept of an...
. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have socalled
naked singularitiesIn general relativity, a naked singularity is a gravitational singularity, without an event horizon. In a black hole, there is a region around the singularity, the event horizon, where the gravitational force of the singularity is strong enough so that light cannot escape. Hence, the singularity...
that can be observed from the outside, and hence are deemed
unphysical. The
cosmic censorship hypothesisThe weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of singularities arising in general relativity....
rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter. This is supported by numerical simulations.
Due to the relatively large strength of the
electromagnetic forceElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
, black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a common feature of compact objects. The blackhole candidate binary Xray source
GRS 1915+105GRS 1915+105 or V1487 Aquilae is an Xray binary star system which features a regular star and a black hole. It was discovered on August 15, 1992 by the WATCH allsky monitor aboard Granat. "GRS" stands for "GRANAT source", "1915" is the right ascension and "105" is declination in units of 0.1...
appears to have an angular momentum near the maximum allowed value.
Black hole classifications
Class  Mass  Size 
Supermassive black holeA supermassive black hole is the largest type of black hole in a galaxy, in the order of hundreds of thousands to billions of solar masses. Most, and possibly all galaxies, including the Milky Way, are believed to contain supermassive black holes at their centers.Supermassive black holes have... 
~10^{5}–10^{9} M_{Sun} The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies... 
~0.001–10 AU An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

Intermediatemass black hole An Intermediatemass black hole is a black hole whose mass is significantly more than stellar black holes yet far less than supermassive black holes... 
~10^{3} M_{Sun} 
~10^{3} km = R_{Earth} Because the Earth is not perfectly spherical, no single value serves as its natural radius. Distances from points on the surface to the center range from 6,353 km to 6,384 km...

Stellar black hole A stellar black hole is a black hole formed by the gravitational collapse of a massive star. They have masses ranging from about 3 to several tens of solar masses... 
~10 M_{Sun} 
~30 km 
Micro black hole Micro black holes are tiny black holes, also called quantum mechanical black holes or mini black holes, for which quantum mechanical effects play an important role.... 
up to ~M_{MoonMoonThe Moon is Earth's only known natural satellite,There are a number of nearEarth asteroids including 3753 Cruithne that are coorbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasisatellites and not true moons. For more...} 
up to ~0.1 mm 
Black holes are commonly classified according to their mass, independent of angular momentum
J or electric charge
Q. The size of a black hole, as determined by the radius of the event horizon, or
Schwarzschild radiusThe Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...
, is roughly proportional to the mass
M through
where
r_{sh} is the Schwarzschild radius and
M_{Sun} is the
mass of the SunThe solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...
. This relation is exact only for black holes with zero charge and angular momentum; for more general black holes it can differ up to a factor of 2.
Event horizon
Far away from the black hole a particle can move in any direction, as illustrated by the set of arrows. 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
spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being threedimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
through which matter and light can only pass inward towards the mass of the black hole. Nothing, not even light, can escape from inside the event horizon. The event horizon is referred to as such because if an event occurs within the boundary, information from that event cannot reach an outside observer, making it impossible to determine if such an event occurred.
As predicted by general relativity, the presence of a mass deforms spacetime in such a way that the paths taken by particles bend towards the mass. At the event horizon of a black hole, this deformation becomes so strong that there are no paths that lead away from the black hole.
To a distant observer, clocks near a black hole appear to tick more slowly than those further away from the black hole. Due to this effect, known as
gravitational time dilationGravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential, the more slowly time passes...
, an object falling into a black hole appears to 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 redshiftIn astrophysics, gravitational redshift or Einstein shift describes light or other forms of electromagnetic radiation of certain wavelengths that originate from a source that is in a region of a stronger gravitational field that appear to be of longer wavelength, or redshifted, when seen or...
. 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.
The shape of the event horizon of a black hole is always approximately spherical. For nonrotating (static) black holes the geometry is precisely spherical, while for rotating black holes the sphere is somewhat oblated.
Singularity
At the center of a black hole as described by general relativity lies a
gravitational singularityA gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...
, a region where the spacetime curvature becomes infinite. For a nonrotating black hole this region takes the shape of a single point and for a
rotating black holeA rotating black hole is a black hole that possesses spin angular momentum.Types of black holes:There are four known, exact, black hole solutions to Einstein's equations, which describe gravity in General Relativity. Two of these rotate...
it is smeared out to form a
ring singularityRing singularity is a term used in general relativity to describe the altering gravitational singularity of a rotating black hole, or a Kerr black hole, so that the gravitational singularity becomes shaped like a ring.Description of a ringsingularity:...
lying in the plane of rotation. 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. The singular region can thus be thought of as having infinite density.
Observers falling into a Schwarzschild black hole (i.e. nonrotating and no charges) cannot avoid being carried into the singularity, once they cross the event horizon. They can prolong the experience by accelerating away to slow their descent, but only up to a point; after attaining a certain ideal velocity, it is best to
free fallFree fall is any motion of a body where gravity is the only force acting upon it, at least initially. These conditions produce an inertial trajectory so long as gravity remains the only force. Since this definition does not specify velocity, it also applies to objects initially moving upward...
the rest of the way. When they reach the singularity, they are crushed to infinite density and their mass is added to the total of the black hole. Before that happens, they will have been torn apart by the growing
tidal forceThe tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational force per unit mass exerted on one body by a second body is not constant across its diameter, the side nearest to the second being more attracted by it than the side...
s in a process sometimes referred to as
spaghettificationIn astrophysics, spaghettification is the vertical stretching and horizontal compression of objects into long thin shapes in a very strong gravitational field, and is caused by extreme tidal forces...
or the noodle effect.
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
wormholeIn physics, a wormhole is a hypothetical topological feature of spacetime that would be, fundamentally, a "shortcut" through spacetime. For a simple visual explanation of a wormhole, consider spacetime visualized as a twodimensional surface. If this surface is folded along a third dimension, it...
. The possibility of traveling to another universe is however only theoretical, since any perturbation will destroy this possibility. It also appears to be possible to follow
closed timelike curveIn mathematical physics, a closed timelike curve is a worldline in a Lorentzian manifold, of a material particle in spacetime that is "closed," returning to its starting point...
s (going back to one's own past) around the Kerr singularity, which lead to problems with
causalityCausality is the relationship between causes and effects. It is considered to be fundamental to all natural science, especially physics. Causality is also a topic studied from the perspectives of philosophy and statistics....
like the
grandfather paradoxThe grandfather paradox is a proposed paradox of time travel first described by the science fiction writer René Barjavel in his 1943 book Le Voyageur Imprudent . The paradox is this: suppose a man traveled back in time and killed his biological grandfather before the latter met the traveler's...
. It is expected that none of these peculiar effects would survive in a proper quantum mechanical treatment of rotating and charged black holes.
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 mechanicalQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particlelike and wavelike behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
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 gravityQuantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
will feature black holes without singularities.
Photon sphere
The photon sphere is a spherical boundary of zero thickness such that
photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s moving along
tangentIn geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...
s to the sphere will be trapped in a circular orbit. For nonrotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. The orbits are
dynamically unstableIn numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds...
, 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. 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
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
framedraggingEinstein's general theory of relativity predicts that nonstatic, stationary massenergy distributions affect spacetime in a peculiar way giving rise to a phenomenon usually known as framedragging...
; 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 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 processThe Penrose process is a process theorised by Roger Penrose wherein energy can be extracted from a rotating black hole...
, 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.
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. 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, and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to forming an event horizon.
Once an event horizon forms, Penrose proved that a singularity will form somewhere inside it. Shortly afterwards, Hawking showed that many cosmological solutions describing the
Big BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
have singularities without scalar fields or other exotic matter (see
PenroseHawking singularity theoremsThe Penrose–Hawking singularity theorems are a set of results in general relativity which attempt to answer the question of when gravitation produces singularities.A singularity in solutions of the Einstein field equations is one of two things:...
). The Kerr solution, the nohair theorem and the laws of
black hole thermodynamicsIn physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons...
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 collapseGravitational collapse is the inward fall of a body due to the influence of its own gravity. In any stable body, this gravitational force is counterbalanced by the internal pressure of the body, in the opposite direction to the force of gravity...
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
pressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure. Definition :...
is insufficient to resist the object's own gravity. For stars this usually occurs either because a star has too little "fuel" left to maintain its temperature through
stellar nucleosynthesisStellar nucleosynthesis is the collective term for the nuclear reactions taking place in stars to build the nuclei of the elements heavier than hydrogen. Some small quantity of these reactions also occur on the stellar surface under various circumstances...
, or because a star that would have been stable receives extra matter in a way that does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight. The
ideal gas lawThe ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's 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 stateDegenerate matter is matter that has such extraordinarily high density that the dominant contribution to its pressure is attributable to the Pauli exclusion principle. The pressure maintained by a body of degenerate matter is called the degeneracy pressure, and arises because the Pauli principle...
. The result is one of the various types of
compact starIn astronomy, the term compact star is used to refer collectively to white dwarfs, neutron stars, other exotic dense stars, and black holes. These objects are all small for their mass...
. The type of compact star formed depends on the mass of the remnant—the matter left over after the outer layers have been blown away, such from a
supernovaA supernova is a stellar explosion that is more energetic than a nova. It is pronounced with the plural supernovae or supernovas. Supernovae are extremely luminous and cause a burst of radiation that often briefly outshines an entire galaxy, before fading from view over several weeks or months...
explosion or by pulsations leading to a
planetary nebulaA planetary nebula is an emission nebula consisting of an expanding glowing shell of ionized gas ejected during the asymptotic giant branch phase of certain types of stars late in their life...
. Note that this mass can be substantially less than the original star—remnants exceeding 5 solar masses are produced by stars that were over 20 solar masses before the collapse.
If the mass of the remnant exceeds about 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. No known mechanism (except possibly quark degeneracy pressure, see
quark starA quark star or strange star is a hypothetical type of exotic star composed of quark matter, or strange matter. These are ultradense phases of degenerate matter theorized to form inside particularly massive neutron stars....
) is powerful enough to stop the implosion and the object will inevitably collapse to form a black hole.
The gravitational collapse of heavy stars is assumed to be responsible for the formation of stellar mass black holes.
Star formationStar formation is the process by which dense parts of molecular clouds collapse into a ball of plasma to form a star. As a branch of astronomy star formation includes the study of the interstellar medium and giant molecular clouds as precursors to the star formation process and the study of young...
in the early universe may have resulted in very massive stars, which upon their collapse would have produced black holes of up to 10
^{3} solar masses. These black holes could be the seeds of the supermassive black holes found in the centers of most galaxies.
While most of the energy released during gravitational collapse is emitted very quickly, an outside observer does not actually see the end of this process. Even though the collapse takes a finite amount of time from the
reference frameA frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...
of infalling matter, a distant observer sees the infalling material slow and halt just above the event horizon, due to
gravitational time dilationGravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential, the more slowly time passes...
. Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms is 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 redshifted, eventually fading away.
Primordial black holes in the Big Bang
Gravitational collapse requires great density. In the current epoch of the universe these high densities are only found in stars, but in the early universe shortly after the
big bangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
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 that can then grow under their own gravity. Different models for the early universe vary widely in their predictions of the size of these perturbations. Various models predict the creation of black holes, ranging from a
Planck mass to hundreds of thousands of solar masses. Primordial black holes could thus account for the creation of any type of black hole.
Highenergy collisions
Gravitational collapse is not the only process that could create black holes. In principle, black holes could be formed in highenergy collisions that achieve sufficient density. As of 2002, no such events have been detected, either directly or indirectly as a deficiency of the mass balance in
particle acceleratorA particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in welldefined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...
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 (
m_{P} = ≈ ≈ ), where quantum effects are expected to invalidate the predictions of general relativity. This would put the creation of black holes firmly out of reach of any high energy process occurring on or near the Earth. However, certain developments in quantum gravity suggest that the Planck mass could be much lower: some braneworld scenarios for example put the boundary as low as . This would make it conceivable for
micro black holeMicro black holes are tiny black holes, also called quantum mechanical black holes or mini black holes, for which quantum mechanical effects play an important role....
s to be created in the high energy collisions occurring when
cosmic rayCosmic rays are energetic charged subatomic particles, originating from outer space. They may produce secondary particles that penetrate the Earth's atmosphere and surface. The term ray is historical as cosmic rays were thought to be electromagnetic radiation...
s hit the Earth's atmosphere, or possibly in the new
Large Hadron ColliderThe Large Hadron Collider is the world's largest and highestenergy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....
at
CERNThe European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...
. Yet these theories are very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists. Even if micro black holes should be formed in these collisions, it is expected that they would evaporate in about 10
^{−25} seconds, posing no threat to the Earth.
Growth
Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb gas and interstellar dust from its direct surroundings and omnipresent cosmic background radiation. This is the primary process through which supermassive black holes seem to have grown. A similar process has been suggested for the formation of
intermediatemass black holeAn Intermediatemass black hole is a black hole whose mass is significantly more than stellar black holes yet far less than supermassive black holes...
s in
globular clusterA globular cluster is a spherical collection of stars that orbits a galactic core as a satellite. Globular clusters are very tightly bound by gravity, which gives them their spherical shapes and relatively high stellar densities toward their centers. The name of this category of star cluster is...
s.
Another possibility is for a black hole to merge with other objects such as stars or even other black holes. This is thought to have been important especially for the early development of supermassive black holes, which could have formed from the coagulation of many smaller objects. The process has also been proposed as the origin of some
intermediatemass black holeAn Intermediatemass black hole is a black hole whose mass is significantly more than stellar black holes yet far less than supermassive black holes...
s.
Evaporation
In 1974, Hawking showed that black holes are not entirely black but emit small amounts of thermal radiation. He got this result by applying
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and manybody systems. It is the natural and quantitative language of particle physics and...
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 radiationHawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...
. 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 (the mass possessed by the photons and other particles emitted). Black holes will shrink and evaporate over time. The temperature of this spectrum (Hawking temperature) is proportional to the
surface gravityThe surface gravity, g, of an astronomical or other object is the gravitational acceleration experienced at its surface. The surface gravity may be thought of as the acceleration due to gravity experienced by a hypothetical test particle which is very close to the object's surface and which, in...
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 one solar mass has a Hawking temperature of about 100 nanokelvins. This is far less than the 2.7 K temperature of 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
MoonThe Moon is Earth's only known natural satellite,There are a number of nearEarth asteroids including 3753 Cruithne that are coorbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasisatellites and not true moons. For more...
(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/
c^{2} would take less than 10
^{−88} seconds to evaporate completely. Of course, for such a small black hole
quantum gravitationQuantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
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. NASA's Fermi Gammaray Space Telescope launched in 2008 will continue the search for these flashes.
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
Due to conservation of angular momentum, gas falling into the gravitational well created by a massive object will typically form a disclike 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. In the case of compact objects such as
white dwarfA white dwarf, also called a degenerate dwarf, is a small star composed mostly of electrondegenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored...
s,
neutron starA neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...
s, and black holes, the gas in the inner regions becomes so hot that it will emit vast amounts of radiation (mainly Xrays), which may be detected by telescopes. This process of accretion is one of the most efficient energyproducing processes known; up to 40% of the rest mass of the accreted material can be emitted in radiation. (In nuclear fusion only about 0.7% of the rest mass will be emitted as energy.) In many cases, accretion discs are accompanied by relativistic jets emitted along the poles, which carry away much of the energy. The mechanism for the creation of these jets is currently not well understood.
As such many of the universe's more energetic phenomena have been attributed to the accretion of matter on black holes. In particular,
active galactic nucleiAn active galactic nucleus is a compact region at the centre of a galaxy that has a much higher than normal luminosity over at least some portion, and possibly all, of the electromagnetic spectrum. Such excess emission has been observed in the radio, infrared, optical, ultraviolet, Xray and...
and
quasarA quasistellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were pointlike, similar to stars, rather than...
s are thought to be the accretion discs of supermassive black holes. Similarly, Xray binaries are thought to be
binary starA binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, comes, or secondary...
systems in which one of the two stars is a compact object accreting matter from its companion. It has also been suggested that some
ultraluminous Xray sourceAn ultraluminous Xray source is an astronomical source of Xrays that is less luminous than an active galactic nucleus but is more consistently luminous than any known stellar process , assuming that it radiates isotropically...
s may be the accretion disks of
intermediatemass black holeAn Intermediatemass black hole is a black hole whose mass is significantly more than stellar black holes yet far less than supermassive black holes...
s.
Xray binaries
Xray binaries are
binary starA binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, comes, or secondary...
systems that are luminous in the
XrayXradiation is a form of electromagnetic radiation. Xrays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
part of the spectrum. These Xray emissions are generally thought to be caused by one of the component stars being a compact object accreting matter from the other (regular) star. The presence of an ordinary star in such a system provides a unique opportunity for studying the central object and determining if it might be a black hole.
If such a system emits signals that can be directly traced back to the compact object, it cannot be a black hole. The absence of such a signal does, however, not exclude the possibility that the compact object is a neutron star. By studying the companion star it is often possible to obtain the orbital parameters of the system and obtain an estimate for the mass of the compact object. If this is much larger than the Tolman–Oppenheimer–Volkoff limit (that is, the maximum mass a neutron star can have before collapsing) then the object cannot be a neutron star and is generally expected to be a black hole.
The first strong candidate for a black hole,
Cygnus X1Cygnus X1 is a wellknown galactic Xray source in the constellation Cygnus. It was discovered in 1964 during a rocket flight and is one of the strongest Xray sources seen from Earth, producing a peak Xray flux density of 2.3 Wm−2Hz−1...
, was discovered in this way by
Charles Thomas BoltonCharles Thomas or Tom Bolton is an American astronomer who was the first astronomer to present strong evidence of the existence of a black hole....
, Louise Webster and Paul Murdin in 1972. Some doubt, however, remained due to the uncertainties resultant from the companion star being much heavier than the candidate black hole. Currently, better candidates for black holes are found in a class of Xray binaries called soft Xray transients. In this class of system the companion star is relatively low mass allowing for more accurate estimates in the black hole mass. Moreover, these systems are only active in Xray for several months once every 10–50 years. During the period of low Xray 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 advectiondominated accretion flow
The faintness of the accretion disc during quiescence is thought to be caused by the flow entering a mode called an advectiondominated 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.
Quasiperiodic oscillations
The Xray emission from accretion disks sometimes flickers at certain frequencies. These signals are called
quasiperiodic oscillationsIn Xray astronomy, quasiperiodic oscillation is the manner in which the Xray light from an astronomical object flickers about certain frequencies...
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.
Galactic nuclei
Astronomers use the term "active galaxy" to describe galaxies with unusual characteristics, such as unusual
spectral lineA spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies. Types of line spectra :...
emission and very strong radio emission. Theoretical and observational studies have shown that the activity in these active galactic nuclei (AGN) may be explained by the presence of supermassive black holes. The models of these AGN consist of a central black hole that may be millions or billions of times more massive than the
SunThe Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
; a disk of gas and dust called an accretion disk; and two
jetsRelativistic jets are extremely powerful jets of plasma which emerge from presumed massive objects at the centers of some active galaxies, notably radio galaxies and quasars. Their lengths can reach several thousand or even hundreds of thousands of light years...
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 GalaxyThe Andromeda Galaxy is a spiral galaxy approximately 2.5 million lightyears from Earth in the constellation Andromeda. It is also known as Messier 31, M31, or NGC 224, and is often referred to as the Great Andromeda Nebula in older texts. Andromeda is the nearest spiral galaxy to the...
,
M32Messier 32 is a dwarf elliptical galaxy about 2.65 million lightyears away in the constellation Andromeda. M32 is a satellite galaxy of the famous Andromeda Galaxy and was discovered by Le Gentil in 1749. M32 measures only 6.5 ± 0.2 kly in diameter at the widest point...
, M87,
NGC 3115NGC 3115 is a lenticular galaxy in the constellation Sextans. The galaxy was discovered by William Herschel on February 22, 1787. At about 32 million lightyears away from us it is several times bigger than our Milky Way...
, NGC 3377, NGC 4258, and the
Sombrero GalaxyThe Sombrero Galaxy is an unbarred spiral galaxy in the constellation Virgo located 28 million light years from earth. It has a bright nucleus, an unusually large central bulge, and a prominent dust lane in its inclined disk. The dark dust lane and the bulge give this galaxy the appearance of a...
.
It is now widely accepted that the center of (nearly) every galaxy (not just active ones) contains a supermassive black hole. The close observational correlation between the mass of this hole and the velocity dispersion of the host galaxy's bulge, known as the
Msigma relationThe Msigma relation is an empirical correlation between the stellar velocity dispersion \sigma of a galaxy bulge and the mass M of the supermassive black hole atthe galaxy's center.The relation can be expressed mathematically as...
, strongly suggests a connection between the formation of the black hole and the galaxy itself.
Currently, the best evidence for a supermassive black hole comes from studying the
proper motionThe proper motion of a star is its angular change in position over time as seen from the center of mass of the solar system. It is measured in seconds of arc per year, arcsec/yr, where 3600 arcseconds equal one degree. This contrasts with radial velocity, which is the time rate of change in...
of stars near the center of our own
Milky WayThe Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim unresolved "milky" glowing band arching across the night sky...
. Since 1995 astronomers have tracked the motion of 90 stars in a region called Sagittarius A*. By fitting their motion to Keplerian orbits they were able to infer in 1998 that 2.6 million
solar massThe solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...
es must be contained in a volume with a radius of 0.02 lightyears. Since then one of the stars—called
S2S2, also known as S0—2 , is a star that is located close to the radio source Sagittarius A*, orbiting it with an orbital period of 15.56 ± 0.35 years and a pericenter distance of 17 light hours — about 4 times the distance of Neptune from the Sun.Its changing apparent position has been...
—has completed a full orbit. From the orbital data they were able to place better constraints on the mass and size of the object causing the orbital motion of stars in the Sagittarius A* region, finding that there is a spherical mass of 4.3 million solar masses contained within a radius of less than 0.002 lightyears. While this is more than 3000 times the Schwarzschild radius corresponding to that mass, it is at least consistent with the central object being a supermassive black hole, and no "realistic cluster [of stars] is physically tenable."
Gravitational lensing
The deformation of spacetime around a massive object causes light rays to be deflected much like light passing through an optic
lensA lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
. This phenomenon is known as gravitational lensing. Observations have been made of weak gravitational lensing, in which
photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s are deflected by only a few arcseconds. However, it has never been directly observed for a black hole. 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*.
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 matterIn the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...
could push up this bound. A phase of free
quarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s at high density might allow the existence of dense
quark starA quark star or strange star is a hypothetical type of exotic star composed of quark matter, or strange matter. These are ultradense phases of degenerate matter theorized to form inside particularly massive neutron stars....
s, and some
supersymmetricIn particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
models predict the existence of Q stars. Some extensions of the
standard modelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
posit the existence of
preonIn particle physics, preons are postulated "pointlike" particles, conceived to be subcomponents of quarks and leptons. The word was coined by Jogesh Pati and Abdus Salam in 1974...
s as fundamental building blocks of quarks and
leptonA lepton is an elementary particle and a fundamental constituent of matter. The best known of all leptons is the electron which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons , and neutral...
s, which could hypothetically form preon stars. 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.
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 10
^{8} solar mass black hole is comparable to that of water). 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.
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 mechanicalQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particlelike and wavelike behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
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). In recent years, much attention has been drawn by the fuzzball model in
string theoryString theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
. Based on calculations in specific situations in string theory, the proposal suggest that generically the individual states of a black hole solution do not have an event horizon or singularity, but that for a classical/semiclassical observer the statistical average of such states does appear just like an ordinary black hole in general relativity.
Entropy and thermodynamics
In 1971, Hawking showed under general conditions
[In particular, he assumed that all matter satisfies the weak energy condition.] that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and merge. This result, now known as the second law of black hole mechanics, is remarkably similar to the
second law of thermodynamicsThe second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
, which states that the total
entropyEntropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
of a system can never decrease. As with classical objects at
absolute zeroAbsolute zero is the theoretical temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means....
temperature, it was assumed that black holes had zero entropy. If this were the case, the second law of thermodynamics would be violated by entropyladen matter entering a black hole, resulting in a decrease of the total entropy of the universe. Therefore, Bekenstein proposed that a black hole should have an entropy, and that it should be proportional to its horizon area.
The link with the laws of thermodynamics was further strengthened by Hawking's discovery that
quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and manybody systems. It is the natural and quantitative language of particle physics and...
predicts that a black hole radiates blackbody radiation at a constant temperature. This seemingly causes a violation of the second law of black hole mechanics, since the radiation will carry away energy from the black hole causing it to shrink. The radiation, however also carries away entropy, and it can be proven under general assumptions that the sum of the entropy of the matter surrounding a black hole and one quarter of the area of the horizon as measured in
Planck unitsIn physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units elegantly simplify...
is in fact always increasing. This allows the formulation of the first law of black hole mechanics as an analogue of the
first law of thermodynamicsThe first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...
, with the mass acting as energy, the surface gravity as temperature and the area as entropy.
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 extensive quantity that scales linearly with the volume of the system. This odd property led Gerard 't Hooft and
Leonard SusskindLeonard Susskind is the Felix Bloch Professor of Theoretical Physics at Stanford University. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology...
to propose the
holographic principleThe holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a lightlike boundary like a gravitational horizon...
, which suggests that anything that happens in a volume of spacetime can be described by data on the boundary of that volume.
Although general relativity can be used to perform a semiclassical calculation of black hole entropy, this situation is theoretically unsatisfying. In
statistical mechanicsStatistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
, entropy is understood as counting the number of microscopic configurations of a system that have the same macroscopic qualities (such as
massMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
,
chargeIn physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges are associated with conserved quantum numbers.Formal definition:...
,
pressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure. Definition :...
, etc.). Without a satisfactory theory of
quantum gravityQuantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
, one cannot perform such a computation for black holes. Some progress has been made in various approaches to quantum gravity. In 1995,
Andrew StromingerAndrew Eben Strominger is an American theoretical physicist who works on string theory and son of Jack L. Strominger. He is currently a professor at Harvard University and a senior fellow at the Society of Fellows...
and
Cumrun VafaCumrun Vafa is an IranianAmerican leading string theorist from Harvard University where he started as a Harvard Junior Fellow. He is a recipient of the 2008 Dirac Medal.Birth and education:...
showed that counting the microstates of a specific
supersymmetricIn particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
black hole in
string theoryString theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
reproduced the Bekenstein–Hawking entropy. Since then, similar results have been reported for different black holes both in string theory and in other approaches to quantum gravity like
loop quantum gravityLoop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...
.
Black hole unitarity
An open question in fundamental physics is the socalled information loss paradox, or
black hole unitarityThe black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could disappear in a black hole, allowing many physical states to evolve into the same state...
paradox. Classically, the laws of physics are the same run forward or in reverse (
TsymmetryT Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...
).
Liouville's theoremIn physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics...
dictates conservation of phase space volume, which can be thought of as "conservation of information", so there is some problem even in classical physics. In quantum mechanics, this corresponds to a vital property called
unitarityIn quantum physics, unitarity is a restriction on the allowed evolution of quantum systems that insures the sum of probabilities of all possible outcomes of any event is always 1....
, 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 matrixIn quantum mechanics, a density matrix is a selfadjoint positivesemidefinite matrix of trace one, that describes the statistical state of a quantum system...
).
See also
 Black brane
In general relativity, a black brane is a solution of the equations that generalizes a black hole solution but it is also extended —and translationally symmetric— in p additional spatial dimensions...
 Black hole complementarity
Black hole complementarity is a conjectured solution to the black hole information paradox, proposed by Leonard Susskind and Gerard 't Hooft.Ever since Stephen Hawking suggested information is lost in evaporating black hole once it passes through the event horizon and is inevitably destroyed at the...
 Black holes in fiction
The study of black holes, bodies so massive that even light cannot escape, goes back to the late 18th century, though the term 'black hole' was only coined in 1967...
 Black string
A black string is a higher dimensional generalization of a black hole in which the event horizon is topologically equivalent to S2 × S1 and spacetime is asymptotically Md−1 × S1....
 BTZ black hole
The BTZ black hole, named after Maximo Banados, Claudio Teitelboim, and Jorge Zanelli, is a black hole solution for dimensional gravity with a negative cosmological constant....
 Dumb hole
 Kugelblitz (astrophysics)
In theoretical physics, a kugelblitz is a concentration of light so intense that it forms an event horizon and becomes selftrapped: according to general relativity, if we aim enough radiation into a region, the concentration of energy can warp spacetime enough for the region to become a black...
 List of black holes
 SusskindHawking battle
 Timeline of black hole physics
Timeline of black hole physics* 1640 — Ismael Bullialdus suggests an inversesquare gravitational force law* 1684 — Isaac Newton writes down his inversesquare Law of universal gravitation...
 White hole
A white hole, in general relativity, is a hypothetical region of spacetime which cannot be entered from the outside, but from which matter and light may escape. In this sense it is the reverse of a black hole, which can be entered from the outside, but from which nothing, including light, may escape...
 Wormhole
In physics, a wormhole is a hypothetical topological feature of spacetime that would be, fundamentally, a "shortcut" through spacetime. For a simple visual explanation of a wormhole, consider spacetime visualized as a twodimensional surface. If this surface is folded along a third dimension, it...
Further reading
Popular reading, poem.
University textbooks and monographs, the lecture notes on which the book was based are available for free from Sean Carroll's
website.
Review papers Lecture notes from 2005 SLAC Summer Institute.
External links
Videos