A black hole is an astronomical body so compact that its gravity prevents anything, including light, from escaping. Albert Einstein's theory of general relativity, which describes gravitation as the curvature of spacetime, predicts that any sufficiently compact mass will form a black hole. The boundary of no escape is called the event horizon. In general relativity, crossing a black hole's event horizon traps an object inside but produces no locally detectable change. General relativity also predicts that every black hole should have a central singularity, where the curvature of spacetime is infinite. Objects whose gravitational fields are too strong for light to escape were first considered in the 18th century. In 1916, the first solution of general relativity that would characterise a black hole was found. By the late 1950s, this solution began to be interpreted physically as a region of space from which nothing can escape. Black holes were long considered a mathematical curiosity; it was not until the 1960s that theoretical work showed they were a generic prediction of general relativity. The first widely accepted black hole was Cygnus X-1, an x-ray source proposed as a black hole binary through several studies between 1971 and 1974. Black holes typically form as part of a supernova event when massive stars collapse at the end of their life cycle. After a black hole has formed, it can grow by absorbing mass from its surroundings. Supermassive black holes of millions of solar masses may form by absorbing stars and merging with other black holes, or via direct collapse of gas clouds. There is consensus that supermassive black holes exist in the centres of most galaxies. Quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the rate of emission being inversely proportional to the mass. This causes the black hole to lose mass very slowly, provided it is not accreting matter. However, even the smallest class of black holes observed, stellar black holes, are gaining mass from the cosmic microwave background faster than they are losing mass via Hawking radiation. The presence of a black hole can be inferred through its interaction with matter and electromagnetic radiation such as visible light. Matter falling toward a black hole can form an accretion disk of infalling plasma, heated by friction and emitting light. In extreme cases, this creates a quasar, some of the brightest objects in the universe. Merging black holes can be detected by the gravitational waves they emit. If stars are orbiting a black hole, their motions can be used to determine the black hole's mass and location. 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.
History
The idea of a body so massive that even light could not escape was first proposed in the late 18th century by English astronomer and clergyman John Michell and independently by French scientist Pierre-Simon Laplace. Both scholars proposed very large stars in contrast to the modern concept of an extremely dense object. Michell's idea, in a short part of a letter published in 1784, calculated that a star with the same density but 500 times the radius of the Sun would not let any emitted light escape; the surface escape velocity would exceed the speed of light. Michell correctly hypothesized that such non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies. In 1796, while speculating on the origin of the Solar System in his book Exposition du Système du Monde, Laplace made a qualitative suggestion that a star could be invisible if it were sufficiently large. Franz Xaver von Zach asked Laplace for a mathematical analysis, which Laplace provided and published in von Zach's journal Allgemeine Geographische Ephemeriden.
General relativity
In 1905, Albert Einstein showed that the laws of electromagnetism are identical for observers travelling at different velocities relative to each other. The laws of mechanics had already been shown to be invariant in this way. However, the theory of gravitation was yet to be included. In 1907, Einstein published a paper proposing his equivalence principle, the hypothesis that inertial mass and gravitational mass have a common cause. Using the principle, Einstein predicted the redshift and the lensing effect of gravity on light; his prediction of gravitational lensing was one-half of the value that the full theory of general relativity would predict. By 1915, Einstein refined these ideas into his general theory of relativity, which explained how matter affects spacetime, which in turn affects the motion of other matter. This formed the basis for black hole astrophysics.
Singular solutions in general relativity Only a few months after Einstein published the field equations describing general relativity, astrophysicist Karl Schwarzschild set out to apply the idea to stars. He assumed spherical symmetry with no spin and found a solution to Einstein's equations. A few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, independently gave the same solution. At a certain radius from the centre of the mass, the Schwarzschild solution became singular, meaning that some of the terms in the Einstein equations became infinite. The nature of this radius, which later became known as the Schwarzschild radius, was not understood at the time. Many physicists of the early 20th century were sceptical of the existence of black holes. In a 1926 popular science book, Arthur Eddington critiqued the idea of a star with mass compressed to its Schwarzschild radius as a flaw in the then-poorly-understood theory of general relativity. In 1939, Einstein used his theory of general relativity in an attempt to prove that black holes were impossible. His work relied on increasing pressure or increasing centrifugal force balancing the force of gravity so that the object would not collapse beyond its Schwarzschild radius. He missed the possibility that implosion would drive the system below this critical value.
Gravity vs degeneracy pressure By the 1920s, astronomers had classified a number of white dwarf stars as too cool and dense to be explained by the gradual cooling of ordinary stars. In 1926, Ralph Fowler showed that these stars are not like main-sequence stars, where thermal pressure balances gravity. Instead, a type of quantum-mechanical pressure balances gravity at these temperatures and densities. In 1931, Subrahmanyan Chandrasekhar studied the new state of matter that results from this balance, called electron-degenerate matter, discovering that it is stable below a certain limiting mass. By 1934 he showed that this explained the catalogue of white dwarf stars. When Chandrasekhar announced his results, Eddington pointed out that stars above this limit would radiate until they were sufficiently dense to prevent light from exiting, a conclusion he considered absurd. Eddington and, later, Lev Landau argued that some yet unknown mechanism would stop the collapse. In the 1930s, Fritz Zwicky and Walter Baade studied stellar novae, focusing on exceptionally bright ones they called supernovae. Zwicky promoted the idea that supernovae produced stars with the density of atomic nuclei—neutron stars—but this idea was largely ignored at the time. In 1939, based on Chandrasekhar's reasoning, but working within general relativity rather than Newtonian gravity, J. Robert Oppenheimer and George Volkoff predicted that neutron stars below a certain mass limit, later called the Tolman–Oppenheimer–Volkoff limit, would be stable due to neutron degeneracy pressure. Above that limit, they reasoned that either their model would not apply or that gravitational contraction would not stop. John Archibald Wheeler and two of his students resolved questions about the model behind the Tolman–Oppenheimer–Volkoff (TOV) limit. In 1965, Harrison and Wheeler developed the equations of state relating density to pressure for cold matter all the way through electron degeneracy and neutron degeneracy. Masami Wakano and Wheeler then used the equations to compute the equilibrium curve for stars, relating mass to circumference. They found no additional features that would invalidate the TOV limit. This meant that the only thing that could prevent black holes from forming was a dynamic process ejecting sufficient mass from a star as it cooled.
Birth of modern model The modern concept of black holes was formulated by Robert Oppenheimer and his student Hartland Snyder in 1939. In the paper, Oppenheimer and Snyder solved Einstein's equations of general relativity for an idealised imploding star, in a model later called the Oppenheimer–Snyder model, then described the results from far outside the star. The implosion starts as one might expect: the star material rapidly collapses inward. However, as the density of the star increases, gravitational time dilation increases and the collapse, viewed from afar, seems to slow down further and further until the star reaches its Schwarzschild radius, where it appears frozen in time. In 1958, David Finkelstein identified the Schwarzschild surface as an event horizon, calling it "a perfect unidirectional membrane: causal influences can cross it in only one direction". This means that events that occur inside the black hole cannot affect events that occur outside the black hole. Finkelstein created a new reference frame to include the point of view of infalling observers. Finkelstein's new frame of reference allowed events at the surface of an imploding star to be related to events far away. By 1962 the two points of view were reconciled, convincing many sceptics that implosion into a black hole made physical sense.
Golden age
The era from the mid-1960s to the mid-1970s was the "golden age of black hole research", when general relativity and black holes became mainstream subjects of research. In this period, solutions to the equations of general relativity under various different physical constraints were discovered. 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. In the late 1960s and early 1970s, scientists from research groups formed by Yakov Zeldovich, John Archibald Wheeler and Dennis W. Sciama discovered a series of important mathematical properties of black hole models dubbed "a black hole has no hair" by Wheeler. The first hints came from work by Vitaly Ginzburg who studied a series of increasing compact stars threaded with intense magnetic fields. He discovered that the fields get trapped on the black hole surface. In 1967, Werner Israel showed that any non-spinning, uncharged collapsing star gives a spherically symmetric black hole: any asymmetry must somehow vanish. In 1972, Richard H. Price found that the asymmetry was converted into gravitational waves. It took another 15 years and many physicists to produce a body of work that became known as the no-hair theorem, which states that a stationary black hole is completely described by the three parameters of the Kerr–Newman metric: mass, angular momentum, and electric charge. At first, it was suspected that the strange mathematical singularities found in each of the black hole solutions only appeared due to the assumption that a black hole would be perfectly spherically symmetric, and therefore the singularities would not appear in generic situations where black holes would not necessarily be symmetric. This view was held in particular by Vladimir Belinski, Isaak Khalatnikov, and Evgeny Lifshitz, who tried to prove that no singularities appear in generic solutions, although they would later reverse their positions. However, in 1965, Roger Penrose proved that general relativity predicts that singularities appear in all black holes, although this may not still hold when quantum mechanics is taken into account. Astronomical observations also made great strides during this era. In 1967, Antony Hewish and Jocelyn Bell Burnell discovered pulsars, and by 1969 these were shown to be rapidly rotating neutron stars. 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. However, experimental evidence confirming a black hole was very difficult to obtain and ultimately required efforts from many astronomers. X-ray telescope observations by Riccardo Giacconi's team in 1971 showed that Cygnus X-1 emitted x-rays in rapid, sporadic fashion consistent with a compact source. This became the first candidate black hole. Optical spectroscopy and detailed astrophysical models for Cygnus X-1 were consistent with a binary system of a massive star and compact star generating x-rays as gas from the massive but ordinary star was sucked into its invisible compact companion. (In 2011, the masses of these stars was estimated to be 14.1±1.0 M☉ for the black hole and 19.2±1.9 M☉ for the optical stellar companion.) By 1974 the object was widely considered to be a black hole, but 100% confidence for Cygnus X-1 may not be possible. Work by James Bardeen, Brandon Carter, and Stephen Hawking in the early 1970s led to the formulation of black hole thermodynamics. These laws describe the behaviour of a black hole in a manner analogous to the laws of thermodynamics. Jacob Bekenstein strengthened this analogy with the properties of mass, surface area, and surface gravity for a black hole related to the thermodynamical concepts of energy, entropy, and temperature respectively. 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.
Modern research and observation While Cygnus X-1, a stellar-mass black hole, was generally accepted by the scientific community as a black hole by the end of 1973, it would be decades before a supermassive black hole would gain the same broad recognition. The idea that such objects might exist began with models suggesting that powerful quasars or active galactic nuclei in the centre of galaxies were powered by accreting supermassive black holes. When the Hubble Space Telescope launched in the 1990s, optical studies of the centre of galaxy Messier 87 showed it must have a large concentration of mass. The two candidates for this mass were a black hole and a dense cluster of stars. In 1995, interferometric microwave spectra from the Very Long Baseline Array observed H2O masers as they orbited the centre of NGC 4258, a galaxy with a similar central mass. The orbital parameters ruled out dense stellar clusters as an explanation for galactic nuclei, making supermassive black holes the only plausible explanation. In 1999, David Merritt proposed the M–sigma relation, which related the dispersion of the velocity of matter in the centre bulge of a galaxy to the mass of the supermassive black hole at its core. Subsequent studies confirmed this correlation. Around the same time, based on telescope observations of the velocities of stars at the centre of the Milky Way galaxy, independent work groups led by Andrea Ghez and Reinhard Genzel concluded that the compact radio source in the centre of the galaxy, Sagittarius A*, was likely a supermassive black hole. In late 2015, the LIGO Scientific Collaboration and Virgo Collaboration made the first direct detection of gravitational waves, named GW150914, representing the first observation of a black hole merger. At the time of the merger, the black holes were approximately 1.4 billion light-years away from Earth and had masses roughly 30 and 35 times that of the Sun. In 2017, Rainer Weiss, Kip Thorne, and Barry Barish, who had spearheaded the project, were awarded the Nobel Prize in Physics for their work. Since the initial discovery in 2015, hundreds more gravitational waves have been observed.
On 10 April 2019, the first direct image of a black hole and its vicinity was published, following observations made by the Event Horizon Telescope (EHT) of the supermassive black hole in Messier 87's galactic centre. In 2022, the Event Horizon Telescope collaboration released an image of the black hole in the center of the Milky Way galaxy, Sagittarius A*; the data had been collected in 2017. In 2020, the Nobel Prize in Physics was awarded for work on black holes. Andrea Ghez and Reinhard Genzel shared one-half for their discovery that Sagittarius A* is a supermassive black hole. Penrose received the other half for his work showing that the mathematics of general relativity requires the formation of black holes. Cosmologists lamented that Hawking's extensive theoretical work on black holes would not be honoured, since he had died in 2018 and the Nobel Prize cannot be awarded posthumously.
Etymology In December 1967, someone in the audience reportedly suggested the phrase black hole at a lecture by John Wheeler; Wheeler adopted the term for its brevity and "advertising value", and Wheeler's stature in the field ensured it quickly caught on, leading some to credit Wheeler with coining the phrase. However, the term was used by others around that time. 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. The term was used in print by Life and Science News magazines in 1963, 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.
Definition A black hole is generally defined as a region of spacetime from which no information-carrying signals or objects can escape. However, verifying an object as a black hole by this definition would require waiting for an infinite time and at an infinite distance from the black hole to verify that nothing has escaped, and thus cannot be used to identify a physical black hole. There are several other definitions that can be used to describe or identify black holes, leading to a variety of ways to study them. Astronomical observations measure the mass of objects, and gravitational collapse theories predict that a compact object with a mass larger than three solar masses can only be a black hole: this limit has become the observational definition. A black hole may also be defined as a reservoir of information or a region where space is falling inwards faster than the speed of light.
Properties The no-hair theorem establishes that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, electric charge, and angular momentum; the black hole is otherwise featureless. Any two black holes that share the same values for these properties, or parameters, are indistinguishable from one another. A related no-hair conjecture proposes that dynamic gravitational collapse always results in an object characterized with only these three properties. The conjecture is currently an unsolved problem. The no-hair theorem also makes idealized assumptions in addition to equilibrium that may not apply to astrophysical objects. The simplest equilibrium black hole model with only mass but neither electric charge nor angular momentum is called a Schwarzschild black hole. 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.
Mass
The simplest static black holes have mass but neither electric charge nor angular momentum. Contrary to the popular notion of a black hole "sucking in everything" in its surroundings, from far away, the external gravitational field of a black hole is identical to that of any other body of the same mass. While a black hole can theoretically have any positive mass, its charge and angular momentum are limited by its mass, with this limit being greater for more massive black holes. The net electric charge Q {\displaystyle Q} and the total angular momentum J {\displaystyle J} satisfy the inequality
Q 2 4 π ϵ 0 + c 2 J 2 G M 2 ≤ G M 2 {\displaystyle {\frac {Q^{2}}{4\pi \epsilon _{0}}}+{\frac {c^{2}J^{2}}{GM^{2}}}\leq GM^{2}}
for a black hole of mass M {\displaystyle M} , where ϵ 0 {\displaystyle \epsilon _{0}} is the vacuum permittivity constant, c {\displaystyle c} is the speed of light and G {\displaystyle G} is the gravitational constant. Black holes with the maximum possible combination of charge and spin satisfying this inequality are called extremal black holes. Adding a low-mass object with a lot of charge or angular momentum to an extremal black hole would create a so-called naked singularity, a singularity outside of a black hole. Because these singularities make the universe inherently unpredictable, many physicists believe they could not exist. The weak cosmic censorship hypothesis, proposed by Penrose, rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter. This hypothesis remains an important area of study because has not yet been proven and it relates to many aspects of general relativity and quantum gravity. The total mass of a nearby black hole can be estimated by analysing the motion of the stars or gas surrounding it. The mass of distant supermassive black holes can be inferred from Doppler broadening of spectral lines emitted by rapidly orbiting gas, a technique called reverberation mapping.
Spin and angular momentum All black holes spin, often rapidly. One stellar black hole, GRS 1915+105, has been estimated to spin at over 1,000 revolutions per second. The Milky Way's central black hole Sagittarius A* rotates at about 90% of the maximum possible rate. The spin rate can be inferred from measurements of atomic spectral lines in the X-ray range. As gas near the black hole plunges inward, high energy X-ray emission from electron-positron pairs illuminates the gas further out, appearing red-shifted due to relativistic effects. Depending on the spin of the black hole, this plunge happens at different radii from the hole, with different degrees of redshift. Astronomers can use the gap between the x-ray emission of the outer disk and the redshifted emission from plunging material to determine the spin of the black hole. A newer way to estimate spin is based on the temperature of gases accreting onto the black hole. The method requires an independent measurement of the black hole mass and inclination angle of the accretion disk followed by computer modelling. Gravitational waves from coalescing binary black holes can also provide the spin of both progenitor black holes and the merged hole, but such events are rare. A spinning black hole has angular momentum. The Kerr metric is the solution of Einstein's field equations for a rotating black hole. In addition to the Schwarzschild radius, r S {\displaystyle r_{\textrm {S}}} , it includes a rotational parameter,
a = J M = 2 J r S , {\displaystyle a={\frac {J}{M}}={\frac {2J}{r_{\textrm {S}}}},} where J {\displaystyle J} is the black hole angular momentum. An extremal black hole has | J | = M 2 {\displaystyle |J|=M^{2}} , corresponding to a = 1 {\displaystyle a=1} . The supermassive black hole in the centre of the Messier 87 (M87) galaxy appears to have rotational parameter of 0.90±0.05, very close to the maximum theoretical value.
Charge Black holes are believed to have an approximately neutral charge. For example, Michal Zajaček, Arman Tursunov, Andreas Eckart, and Silke Britzen found the electric charge of Sagittarius A* to be at least ten orders of magnitude below the theoretical maximum. If a black hole were to become charged, particles with an opposite sign of charge would be pulled in by the extra electromagnetic force, while particles with the same sign of charge would be repelled, neutralising the black hole. This effect operates even more rapidly if the black hole is also spinning. A spinning black hole in a magnetic field creates an electric field which would interact with charged particles. Since black holes have so few measurable intrinsic properties, techniques for measuring charge are of interest to astrophysics even if the values may be very small. The charge Q for a nonspinning black hole is bounded by
Q ≤ 4 π ϵ 0 G M , {\displaystyle Q\leq {\sqrt {4\pi \epsilon _{0}G}}M,}
where G is the gravitational constant and M is the black hole's mass.
Classification
Black holes are classified by the theory of their formation and by their mass (expressed in terms of M☉, the mass of the Sun), but these criteria are intertwined. Stellar black holes are formed by stellar collapse. The minimum mass of a black hole formed by stellar gravitational collapse is governed by the maximum mass of a neutron star and is believed to be 2-4 M☉. Hypothetical primordial black holes, believed to have formed soon after the Big Bang, could be far smaller, with masses as little as 10−5 grams at formation. These very small black holes are sometimes called micro black holes. Stellar black holes can have a wide range of masses. Estimates of their maximum mass at formation vary, but generally range from 10-100 M☉, with higher estimates for black holes progenated by low-metallicity stars. Stellar black holes can gain mass via accretion of nearby matter, often from a companion object such as a star or by merger with another black hole. A small number of candidate black holes with masses in the range 102-104 M☉ have been reported. These are larger than stellar black holes but smaller than supermassive black holes, are rarer than either extreme, and are called intermediate-mass black holes. Physicists have speculated that such black holes may form from collisions in globular and star clusters or at the centre of low-mass galaxies. They may also form as the result of mergers of smaller black holes, with several gravitational wave measurements consistent with merged black holes within 110–350 M☉. The black holes with the largest masses are called supermassive black holes, with masses more than 106 M☉. These black holes are believed to exist at the centres of almost every large galaxy, including the Milky Way. Some scientists have proposed a subcategory of even larger black holes, called ultramassive black holes, with masses greater than 109-1010 M☉. Theoretical models predict that the accretion disc that feeds black holes will be unstable once a black hole reaches 50×109–100×109 M☉, setting a rough upper limit to black hole mass.
Structure While black holes are conceptually invisible sinks of all matter and light, in astronomical settings, their enormous gravity alters the motion of surrounding objects and pulls nearby gas inwards at near-light speed, making the area around black holes the brightest objects in the universe.
External geometry
Relativistic jets
Some black holes have relativistic jets—thin streams of plasma travelling away from the black hole at more than 90% of the speed of light. A small fraction of the matter falling towards the black hole gets accelerated away along the hole rotation axis. These jets can extend as far as millions of light-years from the black hole itself. Black holes of any mass can have jets. However, they are typically observed around spinning black holes with strongly-magnetized accretion disks. Relativistic jets were more common in the early universe, when galaxies and their corresponding supermassive black holes were rapidly gaining mass. All black holes with jets also have an accretion disk, but the jets are usually brighter than the disk. Quasars, typically found in other galaxies, are believed to be supermassive black holes with jets; microquasars are believed to be stellar-mass objects with jets, typically observed in the Milky Way. The jets can be powered by either the accretion disk or the rotating black hole spin. While many details of the jets have been studied, no complete model has emerged. One method proposed to fuel these jets is the Blandford-Znajek process, which suggests that the dragging of magnetic field lines by a black hole's rotation could launch jets of matter into space. The Penrose process, which involves extraction of a black hole's rotational energy, has also been proposed as a potential mechanism of jet propulsion. There is evidence that jets at all scales, from microquasars to gamma ray bursts may be produced by a single mechanism.
Accretion disk
Due to conservation of angular momentum, gas falling into the gravitational well created by a massive object will typically form a disk-like structure around the object. As the disk's angular momentum is transferred outward due to processes such as turbulence in the disk, its matter falls farther inward, converting its gravitational energy into heat and releasing a large amount of radiation; absent an explosive event, the radiation pressure limits the accretion rate. The temperature of these disks can range from thousands to millions of kelvins, and temperatures differ throughout a single accretion disk. Accretion disks radiate across the entire electromagnetic spectrum, depending on the disk's turbulence and magnetisation and the black hole's mass and angular momentum. Accretion disks can be defined as geometrically thin or geometrically thick. Geometrically thin disks are mostly confined to the black hole's equatorial plane and have a well-defined edge at the innermost stable circular orbit (ISCO), while geometrically thick disks are supported by internal pressure and temperature and can extend inside the ISCO. Disks with high rates of electron scattering and absorption, appearing bright and opaque, are called optically thick; optically thin disks are more translucent and produce fainter images when viewed from afar. Accretion disks of black holes accreting beyond the Eddington limit are often referred to as polish donuts due to their thick, toroidal shape that resembles that of a donut. Quasar accretion disks are expected to have a "blue spectral shape", meaning that the flux per frequency F ν {\displaystyle F_{\nu }} is proportional to ν 1 / 3 {\displaystyle \nu ^{1/3}} ; this was not originally observed due to emission from dust surrounding the objects. The disk for a stellar black hole, on the other hand, would likely look orange, yellow, or red, with its inner regions being the brightest. Accretion disk colours may also be altered by the Doppler effect, with the part of the disk travelling towards an observer appearing bluer and brighter and the part of the disk travelling away from the observer appearing redder and dimmer.
Innermost stable circular orbit (ISCO)
In Newtonian gravity, test particles can stably orbit at arbitrary distances from a central object. In general relativity, however, there exists a smallest possible radius for which a massive particle can orbit stably. Any infinitesimal inward perturbations to this orbit will lead to the particle spiralling into the black hole, and any outward perturbations will, depending on the energy, cause the particle to spiral in, move to a stable orbit further from the black hole, or escape to infinity. This orbit is called the innermost stable circular orbit, or ISCO. In the case of a Schwarzschild black hole (spin zero) and a particle without spin, the location of the ISCO is:
r I S C O = 3 r s = 6 G M c 2 , {\displaystyle r_{\rm {ISCO}}=3\,r_{\text{s}}={\frac {6\,GM}{c^{2}}},} where r I S C O {\displaystyle r_{\rm {_{ISCO}}}} is the radius of the ISCO, r s {\displaystyle r_{\text{s}}} is the Schwarzschild radius of the black hole, G {\displaystyle G} is the gravitational constant, and c {\displaystyle c} is the speed of light. For spinning black holes, the ISCO is moved inwards for particles orbiting in the same direction that the black hole is spinning (prograde) and outwards for particles orbiting in the opposite direction (retrograde). For example, the ISCO for a particle orbiting retrograde can be as far out as about 4.5 r s {\displaystyle 4.5r_{\text{s}}} , while the ISCO for a particle orbiting prograde can be as close as at the event horizon itself. The radius of this orbit changes slightly based on particle spin. For charged black holes, the ISCO moves inwards.
Photon sphere and shadow
The photon sphere is a spherical boundary for which photons moving on tangents to that sphere are bent completely around the black hole, possibly orbiting multiple times. For Schwarzschild black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. Although light can still escape from the photon sphere, any light that crosses it on an inward trajectory is inevitably captured by the black hole. Consequently, any light reaching a distant observer from the photon sphere must have been emitted by objects located between the photon sphere and the event horizon. Light emitted towards the photon sphere may also curve around the black hole and return to the emitter. For a rotating, uncharged black hole, the radius of the photon sphere depends on the spin parameter and whether the photon is orbiting prograde or retrograde. For a photon orbiting prograde, the photon sphere will be 0.5–1.5 Schwarzschild radii from the centre of the black hole, while for a photon orbiting retrograde, the photon sphere will be between 3–4 Schwarzschild radii from the centre of the black hole. The exact locations of the photon spheres depend on the magnitude of the black hole's rotation. For a charged, nonrotating black hole, there will only be one photon sphere, and the radius of the photon sphere will decrease for increasing black hole charge. For non-extremal, charged, rotating black holes, there will always be two photon spheres, with the exact radii depending on the parameters of the black hole. When viewed from a great distance, the photon sphere creates an observable black hole shadow, a dark silhouette of the black hole against the background stars. Images such as those taken by the Event Horizon Telescope show the black hole shadow, not the event horizon itself. Since no light emerges from within the black hole, this shadow is the limit for possible observations. The shadow of colliding black holes should have characteristic warped shapes, allowing scientists to detect black holes that are about to merge.
Ergosphere
Near a rotating black hole, spacetime rotates similar to a vortex. The rotating spacetime will drag any matter and light into rotation around the spinning black hole. This effect of general relativity, called frame dragging, gets stronger closer to the spinning mass. The region of spacetime in which it is impossible to stay still is called the ergosphere. The ergosphere of a black hole is the region of space bounded by the event horizon and the ergosurface, also known as the stationary limit surface. The ergosurface coincides with the event horizon at the poles but bulges outward around the equator. Matter and radiation can escape from the ergosphere. Through the Penrose process, objects can emerge from the ergosphere with more energy than they entered with. The extra energy is taken from the rotational energy of the black hole, slowing down the rotation of the black hole.
Plunging region
The observable region of spacetime surrounding a black hole closest to its event horizon is known as the plunging region. Within this region, free-falling matter can no longer maintain stable circular orbits or halt its final descent into the black hole. Instead, it rapidly plunges inward at speeds approaching the speed of light, becoming increasingly hot and producing a distinctive, detectable thermal emission. However, light and radiation emitted from this region can still escape from the black hole's gravitational pull.
Radius For a nonspinning, uncharged blac