Black hole

For other uses, see Black hole (disambiguation).

"Frozen star" redirects here. For the hypothetical object, see Frozen star (hypothetical star).

The supermassive black hole at the core of supergiant elliptical galaxy Messier 87, with a mass ~7 billion times the Sun's,^[1] as depicted in the first image released by the Event Horizon Telescope (10 April 2019).^[2][3][4][5] Visible are the crescent-shaped emission ring and central shadow, which are gravitationally magnified views of the black hole's photon ring and the photon capture zone of its event horizon. The crescent shape arises from the black hole's rotation and relativistic beaming; the shadow is about 2.6 times the diameter of the event horizon.^[3]

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A black hole is a region of spacetime exhibiting gravitational attraction so strong that nothing—no particles or even electromagnetic radiation such as light—can escape from it.^[6] The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole.^[7][8] The boundary of the region from which no escape is possible is called the event horizon. Although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, it has no locally detectable features.^[9] In many ways, a black hole acts like an ideal black body, as it reflects no light.^[10][11] Moreover, quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, making it essentially impossible to observe.

Objects whose gravitational fields are too strong for light to escape were first considered in the 18th century by John Michell and Pierre-Simon Laplace.^[12] The first modern solution of general relativity that would characterize a black hole was found by Karl Schwarzschild in 1916, although its interpretation as a region of space from which nothing can escape was first published by David Finkelstein in 1958. Black holes were long considered a mathematical curiosity; it was during the 1960s that theoretical work showed they were a generic prediction of general relativity. The discovery of neutron stars by Jocelyn Bell Burnell in 1967 sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality.

Black holes of stellar mass are expected to form when very massive stars collapse at the end of their life cycle. After a black hole has formed, it can continue to grow by absorbing mass from its surroundings. By absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses (M_☉) may form. There is consensus that supermassive black holes exist in the centers of most galaxies.

The presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as visible light. Matter that falls onto a black hole can form an external accretion disk heated by friction, forming some of the brightest objects in the universe. Stars passing too close to a supermassive black hole can be shred into streamers that shine very brightly before being "swallowed."^[13] If there are other stars orbiting a black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as neutron stars. In this way, astronomers have identified numerous stellar black hole candidates in binary systems, and established that the radio source known as Sagittarius A*, at the core of the Milky Way galaxy, contains a supermassive black hole of about 4.3 million solar masses.

On 11 February 2016, the LIGO collaboration announced the first direct detection of gravitational waves, which also represented the first observation of a black hole merger.^[14] As of December 2018, eleven gravitational wave events have been observed that originated from ten merging black holes (along with one binary neutron star merger).^[15][16] On 10 April 2019, the first ever direct image of a black hole and its vicinity was published, following observations made by the Event Horizon Telescope in 2017 of the supermassive black hole in Messier 87's galactic centre.^[3][17][18]

Simulation of gravitational lensing by a black hole, which distorts the image of a galaxy in the background

Gas cloud being ripped apart by black hole at the centre of the Milky Way (observations from 2006, 2010 and 2013 are shown in blue, green and red, respectively).^[19]

Contents

• 1History
  • 1.1General relativity
    • 1.1.1Golden age
  • 1.2Etymology
• 2Properties and structure
  • 2.1Physical properties
  • 2.2Event horizon
  • 2.3Singularity
  • 2.4Photon sphere
  • 2.5Ergosphere
  • 2.6Innermost stable circular orbit (ISCO)
• 3Formation and evolution
  • 3.1Gravitational collapse
    • 3.1.1Primordial black holes and the Big Bang
  • 3.2High-energy collisions
  • 3.3Growth
  • 3.4Evaporation
• 4Observational evidence
  • 4.1Detection of gravitational waves from merging black holes
  • 4.2Proper motions of stars orbiting Sagittarius A*
  • 4.3Accretion of matter
    • 4.3.1X-ray binaries
    • 4.3.2Galactic nuclei
  • 4.4Microlensing (proposed)
  • 4.5Alternatives
• 5Open questions
  • 5.1Entropy and thermodynamics
  • 5.2Information loss paradox
  • 5.3Firewall paradox
• 6See also
• 7Notes
• 8References
• 9Further reading
• 10External links

History

Simulated view of a black hole in front of the Large Magellanic Cloud. Note the gravitational lensing effect, which produces two enlarged but highly distorted views of the Cloud. Across the top, the Milky Way disk appears distorted into an arc.

The idea of a body so massive that even light could not escape was briefly proposed by astronomical pioneer and English clergyman John Michell in a letter published in November 1784. Michell's simplistic calculations assumed such a body might have the same density as the Sun, and concluded that such a body would form when a star's diameter exceeds the Sun's by a factor of 500, and the surface escape velocity exceeds the usual speed of light. Michell correctly noted that such supermassive but non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies.^[20][12][21] Scholars of the time were initially excited by the proposal that giant but invisible stars might be hiding in plain view, but enthusiasm dampened when the wavelike nature of light became apparent in the early nineteenth century.^[22]

If light were a wave rather than a "corpuscle", it is unclear what, if any, influence gravity would have on escaping light waves.^[12][21] Modern physics discredits Michell's notion of a light ray shooting directly from the surface of a supermassive star, being slowed down by the star's gravity, stopping, and then free-falling back to the star's surface.^[23]

General relativity

See also: History of general relativity

In 1915, Albert Einstein developed his theory of general relativity, having earlier shown that gravity does influence light's motion. Only a few months later, Karl Schwarzschild found a solution to the Einstein field equations, which describes the gravitational field of a point mass and a spherical mass.^[24] A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass and wrote more extensively about its properties.^[25][26] This solution had a peculiar behaviour at what is now called the Schwarzschild radius, where it became singular, meaning that some of the terms in the Einstein equations became infinite. The nature of this surface was not quite understood at the time. In 1924, Arthur Eddington showed that the singularity disappeared after a change of coordinates (see Eddington–Finkelstein coordinates), although it took until 1933 for Georges Lemaître to realize that this meant the singularity at the Schwarzschild radius was a non-physical coordinate singularity.^[27] Arthur Eddington did however comment on the possibility of a star with mass compressed to the Schwarzschild radius in a 1926 book, noting that Einstein's theory allows us to rule out overly large densities for visible stars like Betelgeuse because "a star of 250 million km radius could not possibly have so high a density as the sun. Firstly, the force of gravitation would be so great that light would be unable to escape from it, the rays falling back to the star like a stone to the earth. Secondly, the red shift of the spectral lines would be so great that the spectrum would be shifted out of existence. Thirdly, the mass would produce so much curvature of the space-time metric that space would close up around the star, leaving us outside (i.e., nowhere)."^[28][29]

In 1931, Subrahmanyan Chandrasekhar calculated, using special relativity, that a non-rotating body of electron-degenerate matter above a certain limiting mass (now called the Chandrasekhar limit at 1.4 M_☉) has no stable solutions.^[30] His arguments were opposed by many of his contemporaries like Eddington and Lev Landau, who argued that some yet unknown mechanism would stop the collapse.^[31] They were partly correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star,^[32] which is itself stable. But in 1939, Robert Oppenheimer and others predicted that neutron stars above another limit (the Tolman–Oppenheimer–Volkoff limit) would collapse further 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.^[33] Their original calculations, based on the Pauli exclusion principle, gave it as 0.7 M_☉; subsequent consideration of strong force-mediated neutron-neutron repulsion raised the estimate to approximately 1.5 M_☉ to 3.0 M_☉.^[34] Observations of the neutron star merger GW170817, which is thought to have generated a black hole shortly afterward, have refined the TOV limit estimate to ~2.17 M_☉.^{[35][36][37][38][39]}

Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infalling observers. Because of this property, the collapsed stars were called "frozen stars", because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it to the Schwarzschild radius.^[40]

Golden age

In 1958, David Finkelstein identified the Schwarzschild surface as an event horizon, "a perfect unidirectional membrane: causal influences can cross it in only one direction".^[41] This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. Finkelstein's solution extended the Schwarzschild solution for the future of observers falling into a black hole. A complete extension had already been found by Martin Kruskal, who was urged to publish it.^[42]

These results came at the beginning of the golden age of general relativity, which was marked by general relativity and black holes becoming mainstream subjects of research. This process was helped by the discovery of pulsars by Jocelyn Bell Burnell in 1967,^[43][44] which, by 1969, were shown to be rapidly rotating neutron stars.^[45] 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.^{[citation needed]}

In this period more general black hole solutions were found. In 1963, Roy Kerr found the exact solution for a rotating black hole. Two years later, Ezra Newman found the axisymmetric solution for a black hole that is both rotating and electrically charged.^[46] Through the work of Werner Israel,^[47] Brandon Carter,^[48][49] and David Robinson^[50] the no-hair theorem emerged, stating that a stationary black hole solution is completely described by the three parameters of the Kerr–Newman metric: mass, angular momentum, and electric charge.^[51]

At first, it was suspected that the strange features of the black hole solutions were pathological artifacts from the symmetry conditions imposed, and that the singularities would not appear in generic situations. This view was held in particular by Vladimir Belinsky, Isaak Khalatnikov, and Evgeny Lifshitz, who tried to prove that no singularities appear in generic solutions. However, in the late 1960s Roger Penrose^[52] and Stephen Hawking used global techniques to prove that singularities appear generically.^[53]

Work by James Bardeen, Jacob Bekenstein, Carter, and Hawking in the early 1970s led to the formulation of black hole thermodynamics.^[54] These laws describe the behaviour of a black hole in close analogy to the laws of thermodynamics by relating mass to energy, area to entropy, and surface gravity to temperature. The analogy was completed when Hawking, in 1974, showed that quantum field theory implies that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole, predicting the effect now known as Hawking radiation.^[55]

Etymology

John Michell used the term "dark star",^[56] and in the early 20th century, physicists used the term "gravitationally collapsed object". Science writer Marcia Bartusiak traces the term "black hole" to physicist Robert H. Dicke, who in the early 1960s reportedly compared the phenomenon to the Black Hole of Calcutta, notorious as a prison where people entered but never left alive.^[57]

The term "black hole" was used in print by Life and Science News magazines in 1963,^[57] and by science journalist Ann Ewing in her article "'Black Holes' in Space", dated 18 January 1964, which was a report on a meeting of the American Association for the Advancement of Science held in Cleveland, Ohio.^[58][59]

In December 1967, a student reportedly suggested the phrase "black hole" at a lecture by John Wheeler;^[58] Wheeler adopted the term for its brevity and "advertising value", and it quickly caught on,^[60] leading some to credit Wheeler with coining the phrase.^[61]

Properties and structure

Simple illustration of a non-spinning black hole

The no-hair conjecture postulates that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, charge, and angular momentum; the black hole is otherwise featureless. If the conjecture is true, any two black holes that share the same values for these properties, or parameters, are indistinguishable from one another. The degree to which the conjecture is true for real black holes under the laws of modern physics, is currently an unsolved problem.^[51]

These properties are special because they are visible from outside a black hole. For example, a charged black hole repels other like charges just like any other charged object. Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law, the ADM mass, far away from the black hole.^{[62][clarification needed]} Likewise, the angular momentum can be measured from far away using frame dragging by the gravitomagnetic field.^{[clarification needed]}

When an object falls into a black hole, any information about the shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers. The behavior of the horizon in this situation is a dissipative system that is closely analogous to that of a conductive stretchy membrane with friction and electrical resistance—the membrane paradigm.^[63] This is different from other field theories such as electromagnetism, which do not have any friction or resistivity at the microscopic level, because they are time-reversible. Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in. The information that is lost includes every quantity that cannot be measured far away from the black hole horizon, including approximately conserved quantum numbers such as the total baryon number and lepton number. This behavior is so puzzling that it has been called the black hole information loss paradox.^[64][65]

Gravitational time dilation around a black hole

Physical properties

The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916.^[24] According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.^[66] This means there is no observable difference at a distance 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 correct only near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass.^[67]

Solutions describing more general black holes also exist. Non-rotating charged black holes are described by the Reissner–Nordström metric, while the Kerr metric describes a non-charged rotating black hole. The most general stationary black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum.^[68]

While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. In Planck units, the total electric charge Q and the total angular momentum J are expected to satisfy

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

for a black hole of mass M. Black holes with the minimum possible mass satisfying this inequality are called extremal. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have so-called naked singularities that can be observed from the outside, and hence are deemed unphysical. The cosmic censorship hypothesis rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter.^[7] This is supported by numerical simulations.^[69]

Due to the relatively large strength of the electromagnetic force, black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a universal feature of compact astrophysical objects. The black-hole candidate binary X-ray source GRS 1915+105^[70] appears to have an angular momentum near the maximum allowed value. That uncharged limit is^[71]

${\displaystyle J\leq {\frac {GM^{2}}{c}},}$

allowing definition of a dimensionless spin parameter such that^[71]

${\displaystyle 0\leq {\frac {cJ}{GM^{2}}}\leq 1.}$^{[71][Note 1]}

Black hole classifications

Class	Approx. mass	Approx. radius
Supermassive black hole	105–1010 MSun	0.001–400 AU
Intermediate-mass black hole	103 MSun	103 km ≈ REarth
Stellar black hole	10 MSun	30 km
Micro black hole	up to MMoon	up to 0.1 mm

Black holes are commonly classified according to their mass, independent of angular momentum, J. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is proportional to the mass, M, through

${\displaystyle r_{\mathrm {s} }={\frac {2GM}{c^{2}}}\approx 2.95\,{\frac {M}{M_{\mathrm {Sun} }}}~\mathrm {km,} }$

where r_s is the Schwarzschild radius and M_Sun is the mass of the Sun.^[73] For a black hole with nonzero spin and/or electric charge, the radius is smaller,^{[Note 2]} until an extremal black hole could have an event horizon close to^[74]

${\displaystyle r_{\mathrm {+} }={\frac {GM}{c^{2}}}.}$

Event horizon

Main article: Event horizon

Far away from the black hole, a particle can move in any direction, as illustrated by the set of arrows. It is restricted only by the speed of light.

Closer to the black hole, spacetime starts to deform. There are more paths going towards the black hole than paths moving away.^{[Note 3]}

Inside of the event horizon, all paths bring the particle closer to the center of the black hole. It is no longer possible for the particle to escape.

The defining feature of a black hole is the appearance of an event horizon—a boundary in spacetime through which matter and light can pass only 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 whether such an event occurred.^[76]

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.^[77] 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.^[78]

To a distant observer, clocks near a black hole would appear to tick more slowly than those further away from the black hole.^[79] Due to this effect, known as gravitational time dilation, an object falling into a black hole appears to slow as it approaches the event horizon, taking an infinite time to reach it.^[80] At the same time, all processes on this object slow down, from the view point of a fixed outside observer, causing any light emitted by the object to appear redder and dimmer, an effect known as gravitational redshift.^[81] Eventually, the falling object fades away until it can no longer be seen. Typically this process happens very rapidly with an object disappearing from view within less than a second.^[82]

On the other hand, indestructible observers falling into a black hole do not notice any of these effects as they cross the event horizon. According to their own clocks, which appear to them to tick normally, they cross the event horizon after a finite time without noting any singular behaviour; in classical general relativity, it is impossible to determine the location of the event horizon from local observations, due to Einstein's equivalence principle.^[83][84]

The topology of the event horizon of a black hole at equilibrium is always spherical.^{[Note 4][87]} For non-rotating (static) black holes the geometry of the event horizon is precisely spherical, while for rotating black holes the event horizon is oblate.^[88][89][90]

Singularity

Main article: Gravitational singularity

At the center of a black hole, as described by general relativity, may lie a gravitational singularity, a region where the spacetime curvature becomes infinite.^[91] For a non-rotating black hole, this region takes the shape of a single point and for a rotating black hole, it is smeared out to form a ring singularity that lies in the plane of rotation.^[92] 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.^[93] The singular region can thus be thought of as having infinite density.^[94]

Observers falling into a Schwarzschild black hole (i.e., non-rotating and not charged) 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 limit.^[95] When they reach the singularity, they are crushed to infinite density and their mass is added to the total of the black hole. Before that happens, they will have been torn apart by the growing tidal forces in a process sometimes referred to as spaghettification or the "noodle effect".^[96]

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 wormhole.^[97] The possibility of traveling to another universe is, however, only theoretical since any perturbation would destroy this possibility.^[98] It also appears to be possible to follow closed timelike curves (returning to one's own past) around the Kerr singularity, which leads to problems with causality like the grandfather paradox.^[99] It is expected that none of these peculiar effects would survive in a proper quantum treatment of rotating and charged black holes.^[100]

The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory.^[101] This breakdown, however, is expected; it occurs in a situation where quantum 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, although there exist attempts to formulate such a theory of quantum gravity. It is generally expected that such a theory will not feature any singularities.^[102][103]

Photon sphere

Main article: Photon sphere

The photon sphere is a spherical boundary of zero thickness in which photons that move on tangents to that sphere would be trapped in a circular orbit about the black hole. For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. Their orbits would be dynamically unstable, hence any small perturbation, such as a particle of infalling matter, would cause an instability that would grow over time, either setting the photon on an outward trajectory causing it to escape the black hole, or on an inward spiral where it would eventually cross the event horizon.^[104]

While light can still escape from the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light that reaches an outside observer from the photon sphere must have been emitted by objects between the photon sphere and the event horizon.^[104]

Ergosphere

Main article: Ergosphere

The ergosphere is a pumpkin-shaped region outside of the event horizon, where objects cannot remain stationary.^[105]

Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This is the result of a process known as frame-dragging; general relativity predicts that any rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it. Any object near the rotating mass will tend to start moving in the direction of rotation. For a rotating black hole, this effect is 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.^[106]

The ergosphere of a black hole is a volume whose inner boundary is the black hole's oblate spheroid event horizon and a pumpkin-shaped outer boundary, which coincides with the event horizon at the poles but noticeably wider around the equator. The outer boundary is sometimes called the ergosurface.^[105]

Objects and radiation can escape normally from the ergosphere. Through the Penrose process, objects can emerge from the ergosphere with more energy than they entered. This energy is taken from the rotational energy of the black hole causing the latter to slow.^[107] A variation of the Penrose process in the presence of strong magnetic fields, the Blandford–Znajek process is considered a likely mechanism for the enormous luminosity and relativistic jets of quasars and other active galactic nuclei.

Innermost stable circular orbit (ISCO)

Main article: Innermost stable circular orbit

In Newtonian gravity, test particles can stably orbit at arbitrary distances from a central object. In general relativity, however, there exists an innermost stable circular orbit (often called the ISCO), inside of which, any infinitesimal perturbations to a circular orbit will lead to inspiral into the black hole.^[108] The location of the ISCO depends on the spin of the black hole, in the case of a Schwarzschild black hole (spin zero) is:

${\displaystyle r_{isco}=3\,r_{s}={\frac {6\,GM}{c^{2}}},}$

and decreases with increasing black hole spin for particles orbiting in the same direction as the spin.^[109]

Formation and evolution

Given the bizarre character of black holes, it was long questioned whether such objects could actually exist in nature or whether they were merely pathological solutions to Einstein's equations. Einstein himself wrongly thought black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius.^[110] 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,^[111] and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to the formation of an event horizon.^{[citation needed]}

Simulation of two black holes colliding

Penrose demonstrated that once an event horizon forms, general relativity without quantum mechanics requires that a singularity will form within.^[52] Shortly afterwards, Hawking showed that many cosmological solutions that describe the Big Bang have singularities without scalar fields or other exotic matter (see "Penrose–Hawking singularity theorems").^{[clarification needed]} The Kerr solution, the no-hair theorem, and the laws of black hole thermodynamics showed that the physical properties of black holes were simple and comprehensible, making them respectable subjects for research.^[112] Conventional black holes are formed by gravitational collapse of heavy objects such as stars, but they can also in theory be formed by other processes.^[113][114]

Gravitational collapse

Main article: Gravitational collapse

Gravitational collapse occurs when an object's internal pressure is insufficient to resist the object's own gravity. For stars this usually occurs either because a star has too little "fuel" left to maintain its temperature through stellar nucleosynthesis, or because a star that would have been stable receives extra matter in a way that does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight.^[115] The collapse may be stopped by the degeneracy pressure of the star's constituents, allowing the condensation of matter into an exotic denser state. The result is one of the various types of compact star. Which type forms depends on the mass of the remnant of the original star left after the outer layers have been blown away. Such explosions and pulsations lead to planetary nebula.^[116] This mass can be substantially less than the original star. Remnants exceeding 5 M_☉ are produced by stars that were over 20 M_☉ before the collapse.^[115]

If the mass of the remnant exceeds about 3–4 M_☉ (the Tolman–Oppenheimer–Volkoff limit^[33]), 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 star) is powerful enough to stop the implosion and the object will inevitably collapse to form a black hole.^[115]

Artist's impression of supermassive black hole seed^[117]

The gravitational collapse of heavy stars is assumed to be responsible for the formation of stellar mass black holes. Star formation in the early universe may have resulted in very massive stars, which upon their collapse would have produced black holes of up to 10³ M_☉. These black holes could be the seeds of the supermassive black holes found in the centers of most galaxies.^[118] It has further been suggested that supermassive black holes with typical masses of ~10⁵ M_☉ could have formed from the direct collapse of gas clouds in the young universe.^[113] Some candidates for such objects have been found in observations of the young universe.^[113]

While most of the energy released during gravitational collapse is emitted very quickly, an outside observer does not actually see the end of this process. Even though the collapse takes a finite amount of time from the reference frame of infalling matter, a distant observer would see the infalling material slow and halt just above the event horizon, due to gravitational time dilation. Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms delayed an infinite amount of time. Thus the external observer never sees the formation of the event horizon; instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away.^[119]

Primordial black holes and the Big Bang

Gravitational collapse requires great density. In the current epoch of the universe these high densities are found only in stars, but in the early universe shortly after the Big Bang densities were much greater, possibly allowing for the creation of black holes. High density alone is not enough to allow black hole formation since a uniform mass distribution will not allow the mass to bunch up. In order for primordial black holes to have formed in such a dense medium, there must have been initial density perturbations that could then grow under their own gravity. Different models for the early universe vary widely in their predictions of the scale of these fluctuations. Various models predict the creation of primordial black holes ranging in size from a Planck mass to hundreds of thousands of solar masses.^[114]

Despite the early universe being extremely dense—far denser than is usually required to form a black hole—it did not re-collapse into a black hole during the Big Bang. Models for gravitational collapse of objects of relatively constant size, such as stars, do not necessarily apply in the same way to rapidly expanding space such as the Big Bang.^[120]

High-energy collisions

Simulated event in the CMS detector: a collision in which a micro black hole may be created

Gravitational collapse is not the only process that could create black holes. In principle, black holes could be formed in high-energy 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 accelerator experiments.^[121] 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=√ħ c/G ≈ 1.2×10¹⁹ GeV/c² ≈ 2.2×10⁻⁸ kg), where quantum effects are expected to invalidate the predictions of general relativity.^[122] 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 1 TeV/c².^[123] This would make it conceivable for micro black holes to be created in the high-energy collisions that occur when cosmic rays hit the Earth's atmosphere, or possibly in the Large Hadron Collider at CERN. These theories are very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists.^[124] Even if micro black holes could be formed, it is expected that they would evaporate in about 10⁻²⁵ seconds, posing no threat to the Earth.^[125]

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 surroundings. This is the primary process through which supermassive black holes seem to have grown.^[118] A similar process has been suggested for the formation of intermediate-mass black holes found in globular clusters.^[126] Black holes can also merge with other objects such as stars or even other black holes. This is thought to have been important, especially in the early growth of supermassive black holes, which could have formed from the aggregation of many smaller objects.^[118] The process has also been proposed as the origin of some intermediate-mass black holes.^[127][128]

Evaporation

Main article: Hawking radiation

In 1974, Hawking predicted that black holes are not entirely black but emit small amounts of thermal radiation at a temperature ℏ c³/(8 π G M k_B);^[55] this effect has become known as Hawking radiation. By applying quantum field theory to a static black hole background, he determined that a black hole should emit particles that display a perfect black body spectrum. Since Hawking's publication, many others have verified the result through various approaches.^[129] If Hawking's theory of black hole radiation is correct, then black holes are expected to shrink and evaporate over time as they lose mass by the emission of photons and other particles.^[55] The temperature of this thermal spectrum (Hawking temperature) is proportional to the surface gravity of the black hole, which, for a Schwarzschild black hole, is inversely proportional to the mass. Hence, large black holes emit less radiation than small black holes.^[130]

A stellar black hole of 1 M_☉ has a Hawking temperature of 62 nanokelvins.^[131] This is far less than the 2.7 K temperature of the cosmic microwave background radiation. Stellar-mass or larger black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and thus will grow instead of shrinking.^[132] To have a Hawking temperature larger than 2.7 K (and be able to evaporate), a black hole would need a mass less than the Moon. Such a black hole would have a diameter of less than a tenth of a millimeter.^[133]

If a black hole is very small, the radiation effects are expected to become very strong. A black hole with the mass of a car would have a diameter of about 10⁻²⁴ m and take a nanosecond to evaporate, during which time it would briefly have a luminosity of more than 200 times that of the Sun. Lower-mass black holes are expected to evaporate even faster; for example, a black hole of mass 1 TeV/c² would take less than 10⁻⁸⁸ seconds to evaporate completely. For such a small black hole, quantum gravitation effects are expected to play an important role and could hypothetically make such a small black hole stable, although current developments in quantum gravity do not indicate this is the case.^[134][135]

The Hawking radiation for an astrophysical black hole is predicted to be very weak and would thus be exceedingly difficult to detect from Earth. A possible exception, however, is the burst of gamma rays emitted in the last stage of the evaporation of primordial black holes. Searches for such flashes have proven unsuccessful and provide stringent limits on the possibility of existence of low mass primordial black holes.^[136] NASA's Fermi Gamma-ray Space Telescope launched in 2008 will continue the search for these flashes.^[137]

If black holes evaporate via Hawking radiation, a solar mass black hole will evaporate (beginning once the temperature of the cosmic microwave background drops below that of the black hole) over a period of 10⁶⁴ years.^[138] A supermassive black hole with a mass of 10¹¹ (100 billion) M_☉ will evaporate in around 2×10¹⁰⁰ years.^[139] Some monster black holes in the universe are predicted to continue to grow up to perhaps 10¹⁴ M_☉ during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 10¹⁰⁶ years.^[138]For other uses, see Black hole (disambiguation).

"Frozen star" redirects here. For the hypothetical object, see Frozen star (hypothetical star).

The supermassive black hole at the core of supergiant elliptical galaxy Messier 87, with a mass ~7 billion times the Sun's,^[1] as depicted in the first image released by the Event Horizon Telescope (10 April 2019).^[2][3][4][5] Visible are the crescent-shaped emission ring and central shadow, which are gravitationally magnified views of the black hole's photon ring and the photon capture zone of its event horizon. The crescent shape arises from the black hole's rotation and relativistic beaming; the shadow is about 2.6 times the diameter of the event horizon.^[3]

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A black hole is a region of spacetime exhibiting gravitational attraction so strong that nothing—no particles or even electromagnetic radiation such as light—can escape from it.^[6] The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole.^[7][8] The boundary of the region from which no escape is possible is called the event horizon. Although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, it has no locally detectable features.^[9] In many ways, a black hole acts like an ideal black body, as it reflects no light.^[10][11] Moreover, quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, making it essentially impossible to observe.

Objects whose gravitational fields are too strong for light to escape were first considered in the 18th century by John Michell and Pierre-Simon Laplace.^[12] The first modern solution of general relativity that would characterize a black hole was found by Karl Schwarzschild in 1916, although its interpretation as a region of space from which nothing can escape was first published by David Finkelstein in 1958. Black holes were long considered a mathematical curiosity; it was during the 1960s that theoretical work showed they were a generic prediction of general relativity. The discovery of neutron stars by Jocelyn Bell Burnell in 1967 sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality.

Black holes of stellar mass are expected to form when very massive stars collapse at the end of their life cycle. After a black hole has formed, it can continue to grow by absorbing mass from its surroundings. By absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses (M_☉) may form. There is consensus that supermassive black holes exist in the centers of most galaxies.

The presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as visible light. Matter that falls onto a black hole can form an external accretion disk heated by friction, forming some of the brightest objects in the universe. Stars passing too close to a supermassive black hole can be shred into streamers that shine very brightly before being "swallowed."^[13] If there are other stars orbiting a black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as neutron stars. In this way, astronomers have identified numerous stellar black hole candidates in binary systems, and established that the radio source known as Sagittarius A*, at the core of the Milky Way galaxy, contains a supermassive black hole of about 4.3 million solar masses.

On 11 February 2016, the LIGO collaboration announced the first direct detection of gravitational waves, which also represented the first observation of a black hole merger.^[14] As of December 2018, eleven gravitational wave events have been observed that originated from ten merging black holes (along with one binary neutron star merger).^[15][16] On 10 April 2019, the first ever direct image of a black hole and its vicinity was published, following observations made by the Event Horizon Telescope in 2017 of the supermassive black hole in Messier 87's galactic centre.^[3][17][18]

Simulation of gravitational lensing by a black hole, which distorts the image of a galaxy in the background

Gas cloud being ripped apart by black hole at the centre of the Milky Way (observations from 2006, 2010 and 2013 are shown in blue, green and red, respectively).^[19]

Contents

• 1History
  • 1.1General relativity
    • 1.1.1Golden age
  • 1.2Etymology
• 2Properties and structure
  • 2.1Physical properties
  • 2.2Event horizon
  • 2.3Singularity
  • 2.4Photon sphere
  • 2.5Ergosphere
  • 2.6Innermost stable circular orbit (ISCO)
• 3Formation and evolution
  • 3.1Gravitational collapse
    • 3.1.1Primordial black holes and the Big Bang
  • 3.2High-energy collisions
  • 3.3Growth
  • 3.4Evaporation
• 4Observational evidence
  • 4.1Detection of gravitational waves from merging black holes
  • 4.2Proper motions of stars orbiting Sagittarius A*
  • 4.3Accretion of matter
    • 4.3.1X-ray binaries
    • 4.3.2Galactic nuclei
  • 4.4Microlensing (proposed)
  • 4.5Alternatives
• 5Open questions
  • 5.1Entropy and thermodynamics
  • 5.2Information loss paradox
  • 5.3Firewall paradox
• 6See also
• 7Notes
• 8References
• 9Further reading
• 10External links

History

Simulated view of a black hole in front of the Large Magellanic Cloud. Note the gravitational lensing effect, which produces two enlarged but highly distorted views of the Cloud. Across the top, the Milky Way disk appears distorted into an arc.

The idea of a body so massive that even light could not escape was briefly proposed by astronomical pioneer and English clergyman John Michell in a letter published in November 1784. Michell's simplistic calculations assumed such a body might have the same density as the Sun, and concluded that such a body would form when a star's diameter exceeds the Sun's by a factor of 500, and the surface escape velocity exceeds the usual speed of light. Michell correctly noted that such supermassive but non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies.^[20][12][21] Scholars of the time were initially excited by the proposal that giant but invisible stars might be hiding in plain view, but enthusiasm dampened when the wavelike nature of light became apparent in the early nineteenth century.^[22]

If light were a wave rather than a "corpuscle", it is unclear what, if any, influence gravity would have on escaping light waves.^[12][21] Modern physics discredits Michell's notion of a light ray shooting directly from the surface of a supermassive star, being slowed down by the star's gravity, stopping, and then free-falling back to the star's surface.^[23]

General relativity

See also: History of general relativity

In 1915, Albert Einstein developed his theory of general relativity, having earlier shown that gravity does influence light's motion. Only a few months later, Karl Schwarzschild found a solution to the Einstein field equations, which describes the gravitational field of a point mass and a spherical mass.^[24] A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass and wrote more extensively about its properties.^[25][26] This solution had a peculiar behaviour at what is now called the Schwarzschild radius, where it became singular, meaning that some of the terms in the Einstein equations became infinite. The nature of this surface was not quite understood at the time. In 1924, Arthur Eddington showed that the singularity disappeared after a change of coordinates (see Eddington–Finkelstein coordinates), although it took until 1933 for Georges Lemaître to realize that this meant the singularity at the Schwarzschild radius was a non-physical coordinate singularity.^[27] Arthur Eddington did however comment on the possibility of a star with mass compressed to the Schwarzschild radius in a 1926 book, noting that Einstein's theory allows us to rule out overly large densities for visible stars like Betelgeuse because "a star of 250 million km radius could not possibly have so high a density as the sun. Firstly, the force of gravitation would be so great that light would be unable to escape from it, the rays falling back to the star like a stone to the earth. Secondly, the red shift of the spectral lines would be so great that the spectrum would be shifted out of existence. Thirdly, the mass would produce so much curvature of the space-time metric that space would close up around the star, leaving us outside (i.e., nowhere)."^[28][29]

In 1931, Subrahmanyan Chandrasekhar calculated, using special relativity, that a non-rotating body of electron-degenerate matter above a certain limiting mass (now called the Chandrasekhar limit at 1.4 M_☉) has no stable solutions.^[30] His arguments were opposed by many of his contemporaries like Eddington and Lev Landau, who argued that some yet unknown mechanism would stop the collapse.^[31] They were partly correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star,^[32] which is itself stable. But in 1939, Robert Oppenheimer and others predicted that neutron stars above another limit (the Tolman–Oppenheimer–Volkoff limit) would collapse further 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.^[33] Their original calculations, based on the Pauli exclusion principle, gave it as 0.7 M_☉; subsequent consideration of strong force-mediated neutron-neutron repulsion raised the estimate to approximately 1.5 M_☉ to 3.0 M_☉.^[34] Observations of the neutron star merger GW170817, which is thought to have generated a black hole shortly afterward, have refined the TOV limit estimate to ~2.17 M_☉.^{[35][36][37][38][39]}

Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infalling observers. Because of this property, the collapsed stars were called "frozen stars", because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it to the Schwarzschild radius.^[40]

Golden age

In 1958, David Finkelstein identified the Schwarzschild surface as an event horizon, "a perfect unidirectional membrane: causal influences can cross it in only one direction".^[41] This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. Finkelstein's solution extended the Schwarzschild solution for the future of observers falling into a black hole. A complete extension had already been found by Martin Kruskal, who was urged to publish it.^[42]

These results came at the beginning of the golden age of general relativity, which was marked by general relativity and black holes becoming mainstream subjects of research. This process was helped by the discovery of pulsars by Jocelyn Bell Burnell in 1967,^[43][44] which, by 1969, were shown to be rapidly rotating neutron stars.^[45] 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.^{[citation needed]}

In this period more general black hole solutions were found. In 1963, Roy Kerr found the exact solution for a rotating black hole. Two years later, Ezra Newman found the axisymmetric solution for a black hole that is both rotating and electrically charged.^[46] Through the work of Werner Israel,^[47] Brandon Carter,^[48][49] and David Robinson^[50] the no-hair theorem emerged, stating that a stationary black hole solution is completely described by the three parameters of the Kerr–Newman metric: mass, angular momentum, and electric charge.^[51]

At first, it was suspected that the strange features of the black hole solutions were pathological artifacts from the symmetry conditions imposed, and that the singularities would not appear in generic situations. This view was held in particular by Vladimir Belinsky, Isaak Khalatnikov, and Evgeny Lifshitz, who tried to prove that no singularities appear in generic solutions. However, in the late 1960s Roger Penrose^[52] and Stephen Hawking used global techniques to prove that singularities appear generically.^[53]

Work by James Bardeen, Jacob Bekenstein, Carter, and Hawking in the early 1970s led to the formulation of black hole thermodynamics.^[54] These laws describe the behaviour of a black hole in close analogy to the laws of thermodynamics by relating mass to energy, area to entropy, and surface gravity to temperature. The analogy was completed when Hawking, in 1974, showed that quantum field theory implies that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole, predicting the effect now known as Hawking radiation.^[55]

Etymology

John Michell used the term "dark star",^[56] and in the early 20th century, physicists used the term "gravitationally collapsed object". Science writer Marcia Bartusiak traces the term "black hole" to physicist Robert H. Dicke, who in the early 1960s reportedly compared the phenomenon to the Black Hole of Calcutta, notorious as a prison where people entered but never left alive.^[57]

The term "black hole" was used in print by Life and Science News magazines in 1963,^[57] and by science journalist Ann Ewing in her article "'Black Holes' in Space", dated 18 January 1964, which was a report on a meeting of the American Association for the Advancement of Science held in Cleveland, Ohio.^[58][59]

In December 1967, a student reportedly suggested the phrase "black hole" at a lecture by John Wheeler;^[58] Wheeler adopted the term for its brevity and "advertising value", and it quickly caught on,^[60] leading some to credit Wheeler with coining the phrase.^[61]

Properties and structure

Simple illustration of a non-spinning black hole

The no-hair conjecture postulates that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, charge, and angular momentum; the black hole is otherwise featureless. If the conjecture is true, any two black holes that share the same values for these properties, or parameters, are indistinguishable from one another. The degree to which the conjecture is true for real black holes under the laws of modern physics, is currently an unsolved problem.^[51]

These properties are special because they are visible from outside a black hole. For example, a charged black hole repels other like charges just like any other charged object. Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law, the ADM mass, far away from the black hole.^{[62][clarification needed]} Likewise, the angular momentum can be measured from far away using frame dragging by the gravitomagnetic field.^{[clarification needed]}

When an object falls into a black hole, any information about the shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers. The behavior of the horizon in this situation is a dissipative system that is closely analogous to that of a conductive stretchy membrane with friction and electrical resistance—the membrane paradigm.^[63] This is different from other field theories such as electromagnetism, which do not have any friction or resistivity at the microscopic level, because they are time-reversible. Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in. The information that is lost includes every quantity that cannot be measured far away from the black hole horizon, including approximately conserved quantum numbers such as the total baryon number and lepton number. This behavior is so puzzling that it has been called the black hole information loss paradox.^[64][65]

Gravitational time dilation around a black hole

Physical properties

The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916.^[24] According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.^[66] This means there is no observable difference at a distance 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 correct only near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass.^[67]

Solutions describing more general black holes also exist. Non-rotating charged black holes are described by the Reissner–Nordström metric, while the Kerr metric describes a non-charged rotating black hole. The most general stationary black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum.^[68]

While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. In Planck units, the total electric charge Q and the total angular momentum J are expected to satisfy

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

for a black hole of mass M. Black holes with the minimum possible mass satisfying this inequality are called extremal. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have so-called naked singularities that can be observed from the outside, and hence are deemed unphysical. The cosmic censorship hypothesis rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter.^[7] This is supported by numerical simulations.^[69]

Due to the relatively large strength of the electromagnetic force, black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a universal feature of compact astrophysical objects. The black-hole candidate binary X-ray source GRS 1915+105^[70] appears to have an angular momentum near the maximum allowed value. That uncharged limit is^[71]

${\displaystyle J\leq {\frac {GM^{2}}{c}},}$

allowing definition of a dimensionless spin parameter such that^[71]

${\displaystyle 0\leq {\frac {cJ}{GM^{2}}}\leq 1.}$^{[71][Note 1]}

Black hole classifications

Class	Approx. mass	Approx. radius
Supermassive black hole	105–1010 MSun	0.001–400 AU
Intermediate-mass black hole	103 MSun	103 km ≈ REarth
Stellar black hole	10 MSun	30 km
Micro black hole	up to MMoon	up to 0.1 mm

Black holes are commonly classified according to their mass, independent of angular momentum, J. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is proportional to the mass, M, through

${\displaystyle r_{\mathrm {s} }={\frac {2GM}{c^{2}}}\approx 2.95\,{\frac {M}{M_{\mathrm {Sun} }}}~\mathrm {km,} }$

where r_s is the Schwarzschild radius and M_Sun is the mass of the Sun.^[73] For a black hole with nonzero spin and/or electric charge, the radius is smaller,^{[Note 2]} until an extremal black hole could have an event horizon close to^[74]

${\displaystyle r_{\mathrm {+} }={\frac {GM}{c^{2}}}.}$

Event horizon

Main article: Event horizon

Far away from the black hole, a particle can move in any direction, as illustrated by the set of arrows. It is restricted only by the speed of light.

Closer to the black hole, spacetime starts to deform. There are more paths going towards the black hole than paths moving away.^{[Note 3]}

Inside of the event horizon, all paths bring the particle closer to the center of the black hole. It is no longer possible for the particle to escape.

The defining feature of a black hole is the appearance of an event horizon—a boundary in spacetime through which matter and light can pass only 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 whether such an event occurred.^[76]

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.^[77] 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.^[78]

To a distant observer, clocks near a black hole would appear to tick more slowly than those further away from the black hole.^[79] Due to this effect, known as gravitational time dilation, an object falling into a black hole appears to slow as it approaches the event horizon, taking an infinite time to reach it.^[80] At the same time, all processes on this object slow down, from the view point of a fixed outside observer, causing any light emitted by the object to appear redder and dimmer, an effect known as gravitational redshift.^[81] Eventually, the falling object fades away until it can no longer be seen. Typically this process happens very rapidly with an object disappearing from view within less than a second.^[82]

On the other hand, indestructible observers falling into a black hole do not notice any of these effects as they cross the event horizon. According to their own clocks, which appear to them to tick normally, they cross the event horizon after a finite time without noting any singular behaviour; in classical general relativity, it is impossible to determine the location of the event horizon from local observations, due to Einstein's equivalence principle.^[83][84]

The topology of the event horizon of a black hole at equilibrium is always spherical.^{[Note 4][87]} For non-rotating (static) black holes the geometry of the event horizon is precisely spherical, while for rotating black holes the event horizon is oblate.^[88][89][90]

Singularity

Main article: Gravitational singularity

At the center of a black hole, as described by general relativity, may lie a gravitational singularity, a region where the spacetime curvature becomes infinite.^[91] For a non-rotating black hole, this region takes the shape of a single point and for a rotating black hole, it is smeared out to form a ring singularity that lies in the plane of rotation.^[92] 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.^[93] The singular region can thus be thought of as having infinite density.^[94]

Observers falling into a Schwarzschild black hole (i.e., non-rotating and not charged) 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 limit.^[95] When they reach the singularity, they are crushed to infinite density and their mass is added to the total of the black hole. Before that happens, they will have been torn apart by the growing tidal forces in a process sometimes referred to as spaghettification or the "noodle effect".^[96]

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 wormhole.^[97] The possibility of traveling to another universe is, however, only theoretical since any perturbation would destroy this possibility.^[98] It also appears to be possible to follow closed timelike curves (returning to one's own past) around the Kerr singularity, which leads to problems with causality like the grandfather paradox.^[99] It is expected that none of these peculiar effects would survive in a proper quantum treatment of rotating and charged black holes.^[100]

The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory.^[101] This breakdown, however, is expected; it occurs in a situation where quantum 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, although there exist attempts to formulate such a theory of quantum gravity. It is generally expected that such a theory will not feature any singularities.^[102][103]

Photon sphere

Main article: Photon sphere

The photon sphere is a spherical boundary of zero thickness in which photons that move on tangents to that sphere would be trapped in a circular orbit about the black hole. For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. Their orbits would be dynamically unstable, hence any small perturbation, such as a particle of infalling matter, would cause an instability that would grow over time, either setting the photon on an outward trajectory causing it to escape the black hole, or on an inward spiral where it would eventually cross the event horizon.^[104]

While light can still escape from the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light that reaches an outside observer from the photon sphere must have been emitted by objects between the photon sphere and the event horizon.^[104]

Ergosphere

Main article: Ergosphere

The ergosphere is a pumpkin-shaped region outside of the event horizon, where objects cannot remain stationary.^[105]

Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This is the result of a process known as frame-dragging; general relativity predicts that any rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it. Any object near the rotating mass will tend to start moving in the direction of rotation. For a rotating black hole, this effect is 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.^[106]

The ergosphere of a black hole is a volume whose inner boundary is the black hole's oblate spheroid event horizon and a pumpkin-shaped outer boundary, which coincides with the event horizon at the poles but noticeably wider around the equator. The outer boundary is sometimes called the ergosurface.^[105]

Objects and radiation can escape normally from the ergosphere. Through the Penrose process, objects can emerge from the ergosphere with more energy than they entered. This energy is taken from the rotational energy of the black hole causing the latter to slow.^[107] A variation of the Penrose process in the presence of strong magnetic fields, the Blandford–Znajek process is considered a likely mechanism for the enormous luminosity and relativistic jets of quasars and other active galactic nuclei.

Innermost stable circular orbit (ISCO)

Main article: Innermost stable circular orbit

In Newtonian gravity, test particles can stably orbit at arbitrary distances from a central object. In general relativity, however, there exists an innermost stable circular orbit (often called the ISCO), inside of which, any infinitesimal perturbations to a circular orbit will lead to inspiral into the black hole.^[108] The location of the ISCO depends on the spin of the black hole, in the case of a Schwarzschild black hole (spin zero) is:

${\displaystyle r_{isco}=3\,r_{s}={\frac {6\,GM}{c^{2}}},}$

and decreases with increasing black hole spin for particles orbiting in the same direction as the spin.^[109]

Formation and evolution

Given the bizarre character of black holes, it was long questioned whether such objects could actually exist in nature or whether they were merely pathological solutions to Einstein's equations. Einstein himself wrongly thought black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius.^[110] 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,^[111] and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to the formation of an event horizon.^{[citation needed]}

Simulation of two black holes colliding

Penrose demonstrated that once an event horizon forms, general relativity without quantum mechanics requires that a singularity will form within.^[52] Shortly afterwards, Hawking showed that many cosmological solutions that describe the Big Bang have singularities without scalar fields or other exotic matter (see "Penrose–Hawking singularity theorems").^{[clarification needed]} The Kerr solution, the no-hair theorem, and the laws of black hole thermodynamics showed that the physical properties of black holes were simple and comprehensible, making them respectable subjects for research.^[112] Conventional black holes are formed by gravitational collapse of heavy objects such as stars, but they can also in theory be formed by other processes.^[113][114]

Gravitational collapse

Main article: Gravitational collapse

Gravitational collapse occurs when an object's internal pressure is insufficient to resist the object's own gravity. For stars this usually occurs either because a star has too little "fuel" left to maintain its temperature through stellar nucleosynthesis, or because a star that would have been stable receives extra matter in a way that does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight.^[115] The collapse may be stopped by the degeneracy pressure of the star's constituents, allowing the condensation of matter into an exotic denser state. The result is one of the various types of compact star. Which type forms depends on the mass of the remnant of the original star left after the outer layers have been blown away. Such explosions and pulsations lead to planetary nebula.^[116] This mass can be substantially less than the original star. Remnants exceeding 5 M_☉ are produced by stars that were over 20 M_☉ before the collapse.^[115]

If the mass of the remnant exceeds about 3–4 M_☉ (the Tolman–Oppenheimer–Volkoff limit^[33]), 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 star) is powerful enough to stop the implosion and the object will inevitably collapse to form a black hole.^[115]

Artist's impression of supermassive black hole seed^[117]

The gravitational collapse of heavy stars is assumed to be responsible for the formation of stellar mass black holes. Star formation in the early universe may have resulted in very massive stars, which upon their collapse would have produced black holes of up to 10³ M_☉. These black holes could be the seeds of the supermassive black holes found in the centers of most galaxies.^[118] It has further been suggested that supermassive black holes with typical masses of ~10⁵ M_☉ could have formed from the direct collapse of gas clouds in the young universe.^[113] Some candidates for such objects have been found in observations of the young universe.^[113]

While most of the energy released during gravitational collapse is emitted very quickly, an outside observer does not actually see the end of this process. Even though the collapse takes a finite amount of time from the reference frame of infalling matter, a distant observer would see the infalling material slow and halt just above the event horizon, due to gravitational time dilation. Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms delayed an infinite amount of time. Thus the external observer never sees the formation of the event horizon; instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away.^[119]

Primordial black holes and the Big Bang

Gravitational collapse requires great density. In the current epoch of the universe these high densities are found only in stars, but in the early universe shortly after the Big Bang densities were much greater, possibly allowing for the creation of black holes. High density alone is not enough to allow black hole formation since a uniform mass distribution will not allow the mass to bunch up. In order for primordial black holes to have formed in such a dense medium, there must have been initial density perturbations that could then grow under their own gravity. Different models for the early universe vary widely in their predictions of the scale of these fluctuations. Various models predict the creation of primordial black holes ranging in size from a Planck mass to hundreds of thousands of solar masses.^[114]

Despite the early universe being extremely dense—far denser than is usually required to form a black hole—it did not re-collapse into a black hole during the Big Bang. Models for gravitational collapse of objects of relatively constant size, such as stars, do not necessarily apply in the same way to rapidly expanding space such as the Big Bang.^[120]

High-energy collisions

Simulated event in the CMS detector: a collision in which a micro black hole may be created

Gravitational collapse is not the only process that could create black holes. In principle, black holes could be formed in high-energy 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 accelerator experiments.^[121] 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=√ħ c/G ≈ 1.2×10¹⁹ GeV/c² ≈ 2.2×10⁻⁸ kg), where quantum effects are expected to invalidate the predictions of general relativity.^[122] 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 1 TeV/c².^[123] This would make it conceivable for micro black holes to be created in the high-energy collisions that occur when cosmic rays hit the Earth's atmosphere, or possibly in the Large Hadron Collider at CERN. These theories are very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists.^[124] Even if micro black holes could be formed, it is expected that they would evaporate in about 10⁻²⁵ seconds, posing no threat to the Earth.^[125]

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 surroundings. This is the primary process through which supermassive black holes seem to have grown.^[118] A similar process has been suggested for the formation of intermediate-mass black holes found in globular clusters.^[126] Black holes can also merge with other objects such as stars or even other black holes. This is thought to have been important, especially in the early growth of supermassive black holes, which could have formed from the aggregation of many smaller objects.^[118] The process has also been proposed as the origin of some intermediate-mass black holes.^[127][128]

Evaporation

Main article: Hawking radiation

In 1974, Hawking predicted that black holes are not entirely black but emit small amounts of thermal radiation at a temperature ℏ c³/(8 π G M k_B);^[55] this effect has become known as Hawking radiation. By applying quantum field theory to a static black hole background, he determined that a black hole should emit particles that display a perfect black body spectrum. Since Hawking's publication, many others have verified the result through various approaches.^[129] If Hawking's theory of black hole radiation is correct, then black holes are expected to shrink and evaporate over time as they lose mass by the emission of photons and other particles.^[55] The temperature of this thermal spectrum (Hawking temperature) is proportional to the surface gravity of the black hole, which, for a Schwarzschild black hole, is inversely proportional to the mass. Hence, large black holes emit less radiation than small black holes.^[130]

A stellar black hole of 1 M_☉ has a Hawking temperature of 62 nanokelvins.^[131] This is far less than the 2.7 K temperature of the cosmic microwave background radiation. Stellar-mass or larger black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and thus will grow instead of shrinking.^[132] To have a Hawking temperature larger than 2.7 K (and be able to evaporate), a black hole would need a mass less than the Moon. Such a black hole would have a diameter of less than a tenth of a millimeter.^[133]

If a black hole is very small, the radiation effects are expected to become very strong. A black hole with the mass of a car would have a diameter of about 10⁻²⁴ m and take a nanosecond to evaporate, during which time it would briefly have a luminosity of more than 200 times that of the Sun. Lower-mass black holes are expected to evaporate even faster; for example, a black hole of mass 1 TeV/c² would take less than 10⁻⁸⁸ seconds to evaporate completely. For such a small black hole, quantum gravitation effects are expected to play an important role and could hypothetically make such a small black hole stable, although current developments in quantum gravity do not indicate this is the case.^[134][135]

The Hawking radiation for an astrophysical black hole is predicted to be very weak and would thus be exceedingly difficult to detect from Earth. A possible exception, however, is the burst of gamma rays emitted in the last stage of the evaporation of primordial black holes. Searches for such flashes have proven unsuccessful and provide stringent limits on the possibility of existence of low mass primordial black holes.^[136] NASA's Fermi Gamma-ray Space Telescope launched in 2008 will continue the search for these flashes.^[137]

If black holes evaporate via Hawking radiation, a solar mass black hole will evaporate (beginning once the temperature of the cosmic microwave background drops below that of the black hole) over a period of 10⁶⁴ years.^[138] A supermassive black hole with a mass of 10¹¹ (100 billion) M_☉ will evaporate in around 2×10¹⁰⁰ years.^[139] Some monster black holes in the universe are predicted to continue to grow up to perhaps 10¹⁴ M_☉ during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 10¹⁰⁶ years.^[138]For other uses, see Black hole (disambiguation).

"Frozen star" redirects here. For the hypothetical object, see Frozen star (hypothetical star).

The supermassive black hole at the core of supergiant elliptical galaxy Messier 87, with a mass ~7 billion times the Sun's,^[1] as depicted in the first image released by the Event Horizon Telescope (10 April 2019).^[2][3][4][5] Visible are the crescent-shaped emission ring and central shadow, which are gravitationally magnified views of the black hole's photon ring and the photon capture zone of its event horizon. The crescent shape arises from the black hole's rotation and relativistic beaming; the shadow is about 2.6 times the diameter of the event horizon.^[3]

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${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={8\pi G \over c^{4}}T_{\mu \nu }}$
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A black hole is a region of spacetime exhibiting gravitational attraction so strong that nothing—no particles or even electromagnetic radiation such as light—can escape from it.^[6] The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole.^[7][8] The boundary of the region from which no escape is possible is called the event horizon. Although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, it has no locally detectable features.^[9] In many ways, a black hole acts like an ideal black body, as it reflects no light.^[10][11] Moreover, quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, making it essentially impossible to observe.

Objects whose gravitational fields are too strong for light to escape were first considered in the 18th century by John Michell and Pierre-Simon Laplace.^[12] The first modern solution of general relativity that would characterize a black hole was found by Karl Schwarzschild in 1916, although its interpretation as a region of space from which nothing can escape was first published by David Finkelstein in 1958. Black holes were long considered a mathematical curiosity; it was during the 1960s that theoretical work showed they were a generic prediction of general relativity. The discovery of neutron stars by Jocelyn Bell Burnell in 1967 sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality.

Black holes of stellar mass are expected to form when very massive stars collapse at the end of their life cycle. After a black hole has formed, it can continue to grow by absorbing mass from its surroundings. By absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses (M_☉) may form. There is consensus that supermassive black holes exist in the centers of most galaxies.

The presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as visible light. Matter that falls onto a black hole can form an external accretion disk heated by friction, forming some of the brightest objects in the universe. Stars passing too close to a supermassive black hole can be shred into streamers that shine very brightly before being "swallowed."^[13] If there are other stars orbiting a black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as neutron stars. In this way, astronomers have identified numerous stellar black hole candidates in binary systems, and established that the radio source known as Sagittarius A*, at the core of the Milky Way galaxy, contains a supermassive black hole of about 4.3 million solar masses.

On 11 February 2016, the LIGO collaboration announced the first direct detection of gravitational waves, which also represented the first observation of a black hole merger.^[14] As of December 2018, eleven gravitational wave events have been observed that originated from ten merging black holes (along with one binary neutron star merger).^[15][16] On 10 April 2019, the first ever direct image of a black hole and its vicinity was published, following observations made by the Event Horizon Telescope in 2017 of the supermassive black hole in Messier 87's galactic centre.^[3][17][18]

Simulation of gravitational lensing by a black hole, which distorts the image of a galaxy in the background

Gas cloud being ripped apart by black hole at the centre of the Milky Way (observations from 2006, 2010 and 2013 are shown in blue, green and red, respectively).^[19]

Contents

• 1History
  • 1.1General relativity
    • 1.1.1Golden age
  • 1.2Etymology
• 2Properties and structure
  • 2.1Physical properties
  • 2.2Event horizon
  • 2.3Singularity
  • 2.4Photon sphere
  • 2.5Ergosphere
  • 2.6Innermost stable circular orbit (ISCO)
• 3Formation and evolution
  • 3.1Gravitational collapse
    • 3.1.1Primordial black holes and the Big Bang
  • 3.2High-energy collisions
  • 3.3Growth
  • 3.4Evaporation
• 4Observational evidence
  • 4.1Detection of gravitational waves from merging black holes
  • 4.2Proper motions of stars orbiting Sagittarius A*
  • 4.3Accretion of matter
    • 4.3.1X-ray binaries
    • 4.3.2Galactic nuclei
  • 4.4Microlensing (proposed)
  • 4.5Alternatives
• 5Open questions
  • 5.1Entropy and thermodynamics
  • 5.2Information loss paradox
  • 5.3Firewall paradox
• 6See also
• 7Notes
• 8References
• 9Further reading
• 10External links

History

Simulated view of a black hole in front of the Large Magellanic Cloud. Note the gravitational lensing effect, which produces two enlarged but highly distorted views of the Cloud. Across the top, the Milky Way disk appears distorted into an arc.

The idea of a body so massive that even light could not escape was briefly proposed by astronomical pioneer and English clergyman John Michell in a letter published in November 1784. Michell's simplistic calculations assumed such a body might have the same density as the Sun, and concluded that such a body would form when a star's diameter exceeds the Sun's by a factor of 500, and the surface escape velocity exceeds the usual speed of light. Michell correctly noted that such supermassive but non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies.^[20][12][21] Scholars of the time were initially excited by the proposal that giant but invisible stars might be hiding in plain view, but enthusiasm dampened when the wavelike nature of light became apparent in the early nineteenth century.^[22]

If light were a wave rather than a "corpuscle", it is unclear what, if any, influence gravity would have on escaping light waves.^[12][21] Modern physics discredits Michell's notion of a light ray shooting directly from the surface of a supermassive star, being slowed down by the star's gravity, stopping, and then free-falling back to the star's surface.^[23]

General relativity

See also: History of general relativity

In 1915, Albert Einstein developed his theory of general relativity, having earlier shown that gravity does influence light's motion. Only a few months later, Karl Schwarzschild found a solution to the Einstein field equations, which describes the gravitational field of a point mass and a spherical mass.^[24] A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution for the point mass and wrote more extensively about its properties.^[25][26] This solution had a peculiar behaviour at what is now called the Schwarzschild radius, where it became singular, meaning that some of the terms in the Einstein equations became infinite. The nature of this surface was not quite understood at the time. In 1924, Arthur Eddington showed that the singularity disappeared after a change of coordinates (see Eddington–Finkelstein coordinates), although it took until 1933 for Georges Lemaître to realize that this meant the singularity at the Schwarzschild radius was a non-physical coordinate singularity.^[27] Arthur Eddington did however comment on the possibility of a star with mass compressed to the Schwarzschild radius in a 1926 book, noting that Einstein's theory allows us to rule out overly large densities for visible stars like Betelgeuse because "a star of 250 million km radius could not possibly have so high a density as the sun. Firstly, the force of gravitation would be so great that light would be unable to escape from it, the rays falling back to the star like a stone to the earth. Secondly, the red shift of the spectral lines would be so great that the spectrum would be shifted out of existence. Thirdly, the mass would produce so much curvature of the space-time metric that space would close up around the star, leaving us outside (i.e., nowhere)."^[28][29]

In 1931, Subrahmanyan Chandrasekhar calculated, using special relativity, that a non-rotating body of electron-degenerate matter above a certain limiting mass (now called the Chandrasekhar limit at 1.4 M_☉) has no stable solutions.^[30] His arguments were opposed by many of his contemporaries like Eddington and Lev Landau, who argued that some yet unknown mechanism would stop the collapse.^[31] They were partly correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star,^[32] which is itself stable. But in 1939, Robert Oppenheimer and others predicted that neutron stars above another limit (the Tolman–Oppenheimer–Volkoff limit) would collapse further 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.^[33] Their original calculations, based on the Pauli exclusion principle, gave it as 0.7 M_☉; subsequent consideration of strong force-mediated neutron-neutron repulsion raised the estimate to approximately 1.5 M_☉ to 3.0 M_☉.^[34] Observations of the neutron star merger GW170817, which is thought to have generated a black hole shortly afterward, have refined the TOV limit estimate to ~2.17 M_☉.^{[35][36][37][38][39]}

Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infalling observers. Because of this property, the collapsed stars were called "frozen stars", because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it to the Schwarzschild radius.^[40]

Golden age

In 1958, David Finkelstein identified the Schwarzschild surface as an event horizon, "a perfect unidirectional membrane: causal influences can cross it in only one direction".^[41] This did not strictly contradict Oppenheimer's results, but extended them to include the point of view of infalling observers. Finkelstein's solution extended the Schwarzschild solution for the future of observers falling into a black hole. A complete extension had already been found by Martin Kruskal, who was urged to publish it.^[42]

These results came at the beginning of the golden age of general relativity, which was marked by general relativity and black holes becoming mainstream subjects of research. This process was helped by the discovery of pulsars by Jocelyn Bell Burnell in 1967,^[43][44] which, by 1969, were shown to be rapidly rotating neutron stars.^[45] 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.^{[citation needed]}

In this period more general black hole solutions were found. In 1963, Roy Kerr found the exact solution for a rotating black hole. Two years later, Ezra Newman found the axisymmetric solution for a black hole that is both rotating and electrically charged.^[46] Through the work of Werner Israel,^[47] Brandon Carter,^[48][49] and David Robinson^[50] the no-hair theorem emerged, stating that a stationary black hole solution is completely described by the three parameters of the Kerr–Newman metric: mass, angular momentum, and electric charge.^[51]

At first, it was suspected that the strange features of the black hole solutions were pathological artifacts from the symmetry conditions imposed, and that the singularities would not appear in generic situations. This view was held in particular by Vladimir Belinsky, Isaak Khalatnikov, and Evgeny Lifshitz, who tried to prove that no singularities appear in generic solutions. However, in the late 1960s Roger Penrose^[52] and Stephen Hawking used global techniques to prove that singularities appear generically.^[53]

Work by James Bardeen, Jacob Bekenstein, Carter, and Hawking in the early 1970s led to the formulation of black hole thermodynamics.^[54] These laws describe the behaviour of a black hole in close analogy to the laws of thermodynamics by relating mass to energy, area to entropy, and surface gravity to temperature. The analogy was completed when Hawking, in 1974, showed that quantum field theory implies that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole, predicting the effect now known as Hawking radiation.^[55]

Etymology

John Michell used the term "dark star",^[56] and in the early 20th century, physicists used the term "gravitationally collapsed object". Science writer Marcia Bartusiak traces the term "black hole" to physicist Robert H. Dicke, who in the early 1960s reportedly compared the phenomenon to the Black Hole of Calcutta, notorious as a prison where people entered but never left alive.^[57]

The term "black hole" was used in print by Life and Science News magazines in 1963,^[57] and by science journalist Ann Ewing in her article "'Black Holes' in Space", dated 18 January 1964, which was a report on a meeting of the American Association for the Advancement of Science held in Cleveland, Ohio.^[58][59]

In December 1967, a student reportedly suggested the phrase "black hole" at a lecture by John Wheeler;^[58] Wheeler adopted the term for its brevity and "advertising value", and it quickly caught on,^[60] leading some to credit Wheeler with coining the phrase.^[61]

Properties and structure

Simple illustration of a non-spinning black hole

The no-hair conjecture postulates that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, charge, and angular momentum; the black hole is otherwise featureless. If the conjecture is true, any two black holes that share the same values for these properties, or parameters, are indistinguishable from one another. The degree to which the conjecture is true for real black holes under the laws of modern physics, is currently an unsolved problem.^[51]

These properties are special because they are visible from outside a black hole. For example, a charged black hole repels other like charges just like any other charged object. Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law, the ADM mass, far away from the black hole.^{[62][clarification needed]} Likewise, the angular momentum can be measured from far away using frame dragging by the gravitomagnetic field.^{[clarification needed]}

When an object falls into a black hole, any information about the shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers. The behavior of the horizon in this situation is a dissipative system that is closely analogous to that of a conductive stretchy membrane with friction and electrical resistance—the membrane paradigm.^[63] This is different from other field theories such as electromagnetism, which do not have any friction or resistivity at the microscopic level, because they are time-reversible. Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in. The information that is lost includes every quantity that cannot be measured far away from the black hole horizon, including approximately conserved quantum numbers such as the total baryon number and lepton number. This behavior is so puzzling that it has been called the black hole information loss paradox.^[64][65]

Gravitational time dilation around a black hole

Physical properties

The simplest static black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916.^[24] According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.^[66] This means there is no observable difference at a distance 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 correct only near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass.^[67]

Solutions describing more general black holes also exist. Non-rotating charged black holes are described by the Reissner–Nordström metric, while the Kerr metric describes a non-charged rotating black hole. The most general stationary black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum.^[68]

While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. In Planck units, the total electric charge Q and the total angular momentum J are expected to satisfy

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

for a black hole of mass M. Black holes with the minimum possible mass satisfying this inequality are called extremal. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have so-called naked singularities that can be observed from the outside, and hence are deemed unphysical. The cosmic censorship hypothesis rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter.^[7] This is supported by numerical simulations.^[69]

Due to the relatively large strength of the electromagnetic force, black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a universal feature of compact astrophysical objects. The black-hole candidate binary X-ray source GRS 1915+105^[70] appears to have an angular momentum near the maximum allowed value. That uncharged limit is^[71]

${\displaystyle J\leq {\frac {GM^{2}}{c}},}$

allowing definition of a dimensionless spin parameter such that^[71]

${\displaystyle 0\leq {\frac {cJ}{GM^{2}}}\leq 1.}$^{[71][Note 1]}

Black hole classifications

Class	Approx. mass	Approx. radius
Supermassive black hole	105–1010 MSun	0.001–400 AU
Intermediate-mass black hole	103 MSun	103 km ≈ REarth
Stellar black hole	10 MSun	30 km
Micro black hole	up to MMoon	up to 0.1 mm

Black holes are commonly classified according to their mass, independent of angular momentum, J. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is proportional to the mass, M, through

${\displaystyle r_{\mathrm {s} }={\frac {2GM}{c^{2}}}\approx 2.95\,{\frac {M}{M_{\mathrm {Sun} }}}~\mathrm {km,} }$

where r_s is the Schwarzschild radius and M_Sun is the mass of the Sun.^[73] For a black hole with nonzero spin and/or electric charge, the radius is smaller,^{[Note 2]} until an extremal black hole could have an event horizon close to^[74]

${\displaystyle r_{\mathrm {+} }={\frac {GM}{c^{2}}}.}$

Event horizon

Main article: Event horizon

Far away from the black hole, a particle can move in any direction, as illustrated by the set of arrows. It is restricted only by the speed of light.

Closer to the black hole, spacetime starts to deform. There are more paths going towards the black hole than paths moving away.^{[Note 3]}

Inside of the event horizon, all paths bring the particle closer to the center of the black hole. It is no longer possible for the particle to escape.

The defining feature of a black hole is the appearance of an event horizon—a boundary in spacetime through which matter and light can pass only 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 whether such an event occurred.^[76]

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.^[77] 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.^[78]

To a distant observer, clocks near a black hole would appear to tick more slowly than those further away from the black hole.^[79] Due to this effect, known as gravitational time dilation, an object falling into a black hole appears to slow as it approaches the event horizon, taking an infinite time to reach it.^[80] At the same time, all processes on this object slow down, from the view point of a fixed outside observer, causing any light emitted by the object to appear redder and dimmer, an effect known as gravitational redshift.^[81] Eventually, the falling object fades away until it can no longer be seen. Typically this process happens very rapidly with an object disappearing from view within less than a second.^[82]

On the other hand, indestructible observers falling into a black hole do not notice any of these effects as they cross the event horizon. According to their own clocks, which appear to them to tick normally, they cross the event horizon after a finite time without noting any singular behaviour; in classical general relativity, it is impossible to determine the location of the event horizon from local observations, due to Einstein's equivalence principle.^[83][84]

The topology of the event horizon of a black hole at equilibrium is always spherical.^{[Note 4][87]} For non-rotating (static) black holes the geometry of the event horizon is precisely spherical, while for rotating black holes the event horizon is oblate.^[88][89][90]

Singularity

Main article: Gravitational singularity

At the center of a black hole, as described by general relativity, may lie a gravitational singularity, a region where the spacetime curvature becomes infinite.^[91] For a non-rotating black hole, this region takes the shape of a single point and for a rotating black hole, it is smeared out to form a ring singularity that lies in the plane of rotation.^[92] 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.^[93] The singular region can thus be thought of as having infinite density.^[94]

Observers falling into a Schwarzschild black hole (i.e., non-rotating and not charged) 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 limit.^[95] When they reach the singularity, they are crushed to infinite density and their mass is added to the total of the black hole. Before that happens, they will have been torn apart by the growing tidal forces in a process sometimes referred to as spaghettification or the "noodle effect".^[96]

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 wormhole.^[97] The possibility of traveling to another universe is, however, only theoretical since any perturbation would destroy this possibility.^[98] It also appears to be possible to follow closed timelike curves (returning to one's own past) around the Kerr singularity, which leads to problems with causality like the grandfather paradox.^[99] It is expected that none of these peculiar effects would survive in a proper quantum treatment of rotating and charged black holes.^[100]

The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory.^[101] This breakdown, however, is expected; it occurs in a situation where quantum 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, although there exist attempts to formulate such a theory of quantum gravity. It is generally expected that such a theory will not feature any singularities.^[102][103]

Photon sphere

Main article: Photon sphere

The photon sphere is a spherical boundary of zero thickness in which photons that move on tangents to that sphere would be trapped in a circular orbit about the black hole. For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. Their orbits would be dynamically unstable, hence any small perturbation, such as a particle of infalling matter, would cause an instability that would grow over time, either setting the photon on an outward trajectory causing it to escape the black hole, or on an inward spiral where it would eventually cross the event horizon.^[104]

While light can still escape from the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light that reaches an outside observer from the photon sphere must have been emitted by objects between the photon sphere and the event horizon.^[104]

Ergosphere

Main article: Ergosphere

The ergosphere is a pumpkin-shaped region outside of the event horizon, where objects cannot remain stationary.^[105]

Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This is the result of a process known as frame-dragging; general relativity predicts that any rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it. Any object near the rotating mass will tend to start moving in the direction of rotation. For a rotating black hole, this effect is 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.^[106]

The ergosphere of a black hole is a volume whose inner boundary is the black hole's oblate spheroid event horizon and a pumpkin-shaped outer boundary, which coincides with the event horizon at the poles but noticeably wider around the equator. The outer boundary is sometimes called the ergosurface.^[105]

Objects and radiation can escape normally from the ergosphere. Through the Penrose process, objects can emerge from the ergosphere with more energy than they entered. This energy is taken from the rotational energy of the black hole causing the latter to slow.^[107] A variation of the Penrose process in the presence of strong magnetic fields, the Blandford–Znajek process is considered a likely mechanism for the enormous luminosity and relativistic jets of quasars and other active galactic nuclei.

Innermost stable circular orbit (ISCO)

Main article: Innermost stable circular orbit

In Newtonian gravity, test particles can stably orbit at arbitrary distances from a central object. In general relativity, however, there exists an innermost stable circular orbit (often called the ISCO), inside of which, any infinitesimal perturbations to a circular orbit will lead to inspiral into the black hole.^[108] The location of the ISCO depends on the spin of the black hole, in the case of a Schwarzschild black hole (spin zero) is:

${\displaystyle r_{isco}=3\,r_{s}={\frac {6\,GM}{c^{2}}},}$

and decreases with increasing black hole spin for particles orbiting in the same direction as the spin.^[109]

Formation and evolution

Given the bizarre character of black holes, it was long questioned whether such objects could actually exist in nature or whether they were merely pathological solutions to Einstein's equations. Einstein himself wrongly thought black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius.^[110] 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,^[111] and by the end of the 1960s, they had persuaded the majority of researchers in the field that there is no obstacle to the formation of an event horizon.^{[citation needed]}

Simulation of two black holes colliding

Penrose demonstrated that once an event horizon forms, general relativity without quantum mechanics requires that a singularity will form within.^[52] Shortly afterwards, Hawking showed that many cosmological solutions that describe the Big Bang have singularities without scalar fields or other exotic matter (see "Penrose–Hawking singularity theorems").^{[clarification needed]} The Kerr solution, the no-hair theorem, and the laws of black hole thermodynamics showed that the physical properties of black holes were simple and comprehensible, making them respectable subjects for research.^[112] Conventional black holes are formed by gravitational collapse of heavy objects such as stars, but they can also in theory be formed by other processes.^[113][114]

Gravitational collapse

Main article: Gravitational collapse

Gravitational collapse occurs when an object's internal pressure is insufficient to resist the object's own gravity. For stars this usually occurs either because a star has too little "fuel" left to maintain its temperature through stellar nucleosynthesis, or because a star that would have been stable receives extra matter in a way that does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight.^[115] The collapse may be stopped by the degeneracy pressure of the star's constituents, allowing the condensation of matter into an exotic denser state. The result is one of the various types of compact star. Which type forms depends on the mass of the remnant of the original star left after the outer layers have been blown away. Such explosions and pulsations lead to planetary nebula.^[116] This mass can be substantially less than the original star. Remnants exceeding 5 M_☉ are produced by stars that were over 20 M_☉ before the collapse.^[115]

If the mass of the remnant exceeds about 3–4 M_☉ (the Tolman–Oppenheimer–Volkoff limit^[33]), 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 star) is powerful enough to stop the implosion and the object will inevitably collapse to form a black hole.^[115]

Artist's impression of supermassive black hole seed^[117]

The gravitational collapse of heavy stars is assumed to be responsible for the formation of stellar mass black holes. Star formation in the early universe may have resulted in very massive stars, which upon their collapse would have produced black holes of up to 10³ M_☉. These black holes could be the seeds of the supermassive black holes found in the centers of most galaxies.^[118] It has further been suggested that supermassive black holes with typical masses of ~10⁵ M_☉ could have formed from the direct collapse of gas clouds in the young universe.^[113] Some candidates for such objects have been found in observations of the young universe.^[113]

While most of the energy released during gravitational collapse is emitted very quickly, an outside observer does not actually see the end of this process. Even though the collapse takes a finite amount of time from the reference frame of infalling matter, a distant observer would see the infalling material slow and halt just above the event horizon, due to gravitational time dilation. Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms delayed an infinite amount of time. Thus the external observer never sees the formation of the event horizon; instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away.^[119]

Primordial black holes and the Big Bang

Gravitational collapse requires great density. In the current epoch of the universe these high densities are found only in stars, but in the early universe shortly after the Big Bang densities were much greater, possibly allowing for the creation of black holes. High density alone is not enough to allow black hole formation since a uniform mass distribution will not allow the mass to bunch up. In order for primordial black holes to have formed in such a dense medium, there must have been initial density perturbations that could then grow under their own gravity. Different models for the early universe vary widely in their predictions of the scale of these fluctuations. Various models predict the creation of primordial black holes ranging in size from a Planck mass to hundreds of thousands of solar masses.^[114]

Despite the early universe being extremely dense—far denser than is usually required to form a black hole—it did not re-collapse into a black hole during the Big Bang. Models for gravitational collapse of objects of relatively constant size, such as stars, do not necessarily apply in the same way to rapidly expanding space such as the Big Bang.^[120]

High-energy collisions

Simulated event in the CMS detector: a collision in which a micro black hole may be created

Gravitational collapse is not the only process that could create black holes. In principle, black holes could be formed in high-energy 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 accelerator experiments.^[121] 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=√ħ c/G ≈ 1.2×10¹⁹ GeV/c² ≈ 2.2×10⁻⁸ kg), where quantum effects are expected to invalidate the predictions of general relativity.^[122] 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 1 TeV/c².^[123] This would make it conceivable for micro black holes to be created in the high-energy collisions that occur when cosmic rays hit the Earth's atmosphere, or possibly in the Large Hadron Collider at CERN. These theories are very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists.^[124] Even if micro black holes could be formed, it is expected that they would evaporate in about 10⁻²⁵ seconds, posing no threat to the Earth.^[125]

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 surroundings. This is the primary process through which supermassive black holes seem to have grown.^[118] A similar process has been suggested for the formation of intermediate-mass black holes found in globular clusters.^[126] Black holes can also merge with other objects such as stars or even other black holes. This is thought to have been important, especially in the early growth of supermassive black holes, which could have formed from the aggregation of many smaller objects.^[118] The process has also been proposed as the origin of some intermediate-mass black holes.^[127][128]

Evaporation

Main article: Hawking radiation

In 1974, Hawking predicted that black holes are not entirely black but emit small amounts of thermal radiation at a temperature ℏ c³/(8 π G M k_B);^[55] this effect has become known as Hawking radiation. By applying quantum field theory to a static black hole background, he determined that a black hole should emit particles that display a perfect black body spectrum. Since Hawking's publication, many others have verified the result through various approaches.^[129] If Hawking's theory of black hole radiation is correct, then black holes are expected to shrink and evaporate over time as they lose mass by the emission of photons and other particles.^[55] The temperature of this thermal spectrum (Hawking temperature) is proportional to the surface gravity of the black hole, which, for a Schwarzschild black hole, is inversely proportional to the mass. Hence, large black holes emit less radiation than small black holes.^[130]

A stellar black hole of 1 M_☉ has a Hawking temperature of 62 nanokelvins.^[131] This is far less than the 2.7 K temperature of the cosmic microwave background radiation. Stellar-mass or larger black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and thus will grow instead of shrinking.^[132] To have a Hawking temperature larger than 2.7 K (and be able to evaporate), a black hole would need a mass less than the Moon. Such a black hole would have a diameter of less than a tenth of a millimeter.^[133]

If a black hole is very small, the radiation effects are expected to become very strong. A black hole with the mass of a car would have a diameter of about 10⁻²⁴ m and take a nanosecond to evaporate, during which time it would briefly have a luminosity of more than 200 times that of the Sun. Lower-mass black holes are expected to evaporate even faster; for example, a black hole of mass 1 TeV/c² would take less than 10⁻⁸⁸ seconds to evaporate completely. For such a small black hole, quantum gravitation effects are expected to play an important role and could hypothetically make such a small black hole stable, although current developments in quantum gravity do not indicate this is the case.^[134][135]

The Hawking radiation for an astrophysical black hole is predicted to be very weak and would thus be exceedingly difficult to detect from Earth. A possible exception, however, is the burst of gamma rays emitted in the last stage of the evaporation of primordial black holes. Searches for such flashes have proven unsuccessful and provide stringent limits on the possibility of existence of low mass primordial black holes.^[136] NASA's Fermi Gamma-ray Space Telescope launched in 2008 will continue the search for these flashes.^[137]

If black holes evaporate via Hawking radiation, a solar mass black hole will evaporate (beginning once the temperature of the cosmic microwave background drops below that of the black hole) over a period of 10⁶⁴ years.^[138] A supermassive black hole with a mass of 10¹¹ (100 billion) M_☉ will evaporate in around 2×10¹⁰⁰ years.^[139] Some monster black holes in the universe are predicted to continue to grow up to perhaps 10¹⁴ M_☉ during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 10¹⁰⁶ years.^[138]