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CONTENTS

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* (Top)
* 1 History
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* 1.1 General relativity
* 1.1.1 Golden age
* 1.2 Observation
* 1.3 Etymology
* 2 Properties and structure
Toggle Properties and structure subsection
* 2.1 Physical properties
* 2.2 Event horizon
* 2.3 Singularity
* 2.4 Photon sphere
* 2.5 Ergosphere
* 2.6 Innermost stable circular orbit (ISCO)
* 2.7 Plunging region
* 3 Formation and evolution
Toggle Formation and evolution subsection
* 3.1 Gravitational collapse
* 3.1.1 Primordial black holes and the Big Bang
* 3.2 High-energy collisions
* 3.3 Growth
* 3.4 Evaporation
* 4 Observational evidence
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* 4.1 Direct interferometry
* 4.2 Detection of gravitational waves from merging black holes
* 4.3 Stars orbiting Sagittarius A*
* 4.4 Accretion of matter
* 4.4.1 X-ray binaries
* 4.4.1.1 Quasi-periodic oscillations
* 4.4.2 Galactic nuclei
* 4.5 Microlensing
* 5 Alternatives
* 6 Open questions
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* 6.1 Entropy and thermodynamics
* 6.2 Information loss paradox
* 7 See also
* 8 Notes
* 9 References
* 10 Sources
* 11 Further reading
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* 11.1 Popular reading
* 11.2 University textbooks and monographs
* 11.3 Review papers
* 12 External links
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* 12.1 Videos

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BLACK HOLE

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From Wikipedia, the free encyclopedia

Object that has a no-return boundary
For other uses, see Black hole (disambiguation).

Direct radio image of a supermassive black hole at the core of Messier 87[1]
Animated simulation of a Schwarzschild black hole with a galaxy passing behind.
Around the time of alignment, extreme gravitational lensing of the galaxy is
observed.

A black hole is a region of spacetime where gravity is so strong that nothing,
not even light and other electromagnetic waves, is capable of possessing enough
energy to escape it.[2] Einstein's theory of general relativity predicts that a
sufficiently compact mass can deform spacetime to form a black hole.[3][4] The
boundary of no escape is called the event horizon. A black hole has a great
effect on the fate and circumstances of an object crossing it, but it has no
locally detectable features according to general relativity.[5] In many ways, a
black hole acts like an ideal black body, as it reflects no light.[6][7] 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 of the order of billionths of a
kelvin for stellar black holes, making it essentially impossible to observe
directly.

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.[8] In
1916, Karl Schwarzschild found the first modern solution of general relativity
that would characterise a black hole. David Finkelstein, in 1958, first
published the interpretation of "black hole" 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 discovery of neutron stars by Jocelyn Bell
Burnell in 1967 sparked interest in gravitationally collapsed compact objects as
a possible astrophysical reality. The first black hole known was Cygnus X-1,
identified by several researchers independently in 1971.[9][10]

Black holes of stellar mass form 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 (M☉) may
form by absorbing other 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.

The presence of a black hole can be inferred through its interaction with other
matter and with electromagnetic radiation such as visible light. Any matter that
falls toward a black hole can form an external accretion disk heated by
friction, forming quasars, some of the brightest objects in the universe. Stars
passing too close to a supermassive black hole can be shredded into streamers
that shine very brightly before being "swallowed."[11] If other stars are
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.

HISTORY

The idea of a body so big that even light could not escape was briefly proposed
by English astronomical pioneer and 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 one would form when a
star's diameter exceeds the Sun's by a factor of 500, and its 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.[8][12][13] Scholars of the time
were initially excited by the proposal that giant but invisible 'dark stars'
might be hiding in plain view, but enthusiasm dampened when the wavelike nature
of light became apparent in the early nineteenth century,[14] as if light were a
wave rather than a particle, it was unclear what, if any, influence gravity
would have on escaping light waves.[8][13]

The modern theory of gravity, general relativity, 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.[15] Instead, spacetime itself is curved such that the geodesic
that light travels on never leaves the surface of the "star" (black hole).

GENERAL RELATIVITY

See also: History of general relativity

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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 that
describes the gravitational field of a point mass and a spherical mass.[16][17]
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.[18][19] 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. In 1933, Georges Lemaître realised that this meant the
singularity at the Schwarzschild radius was a non-physical coordinate
singularity.[20] Arthur Eddington commented 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 spacetime metric that space
would close up around the star, leaving us outside (i.e., nowhere)."[21][22]

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.[23] 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.[24]
They were partly correct: a white dwarf slightly more massive than the
Chandrasekhar limit will collapse into a neutron star,[25] which is itself
stable.

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.[26] Their original calculations, based on the Pauli exclusion principle,
gave it as 0.7 M☉. Subsequent consideration of neutron-neutron repulsion
mediated by the strong force raised the estimate to approximately 1.5 M☉ to
3.0 M☉.[27] 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☉.[28][29][30][31][32]

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. The hypothetical 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.[33]

Also in 1939, Einstein attempted to prove that black holes were impossible in
his publication "On a Stationary System with Spherical Symmetry Consisting of
Many Gravitating Masses", using his theory of general relativity to defend his
argument.[34] Months later, Oppenheimer and his student Hartland Snyder provided
the Oppenheimer–Snyder model in their paper "On Continued Gravitational
Contraction",[35] which predicted the existence of black holes. In the paper,
which made no reference to Einstein's recent publication, Oppenheimer and Snyder
used Einstein's own theory of general relativity to show the conditions on how a
black hole could develop, for the first time in contemporary physics.[34]

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".[36] 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.[37]

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,[38][39] which, by 1969, were shown to be rapidly
rotating neutron stars.[40] 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.[41]

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.[42] Through the work of Werner Israel,[43] Brandon
Carter,[44][45] and David Robinson[46] 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.[47]

At first, it was suspected that the strange features of the black hole solutions
were pathological artefacts 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[48] and Stephen Hawking used global techniques to
prove that singularities appear generically.[49] For this work, Penrose received
half of the 2020 Nobel Prize in Physics, Hawking having died in 2018.[50] Based
on observations in Greenwich and Toronto in the early 1970s, Cygnus X-1, a
galactic X-ray source discovered in 1964, became the first astronomical object
commonly accepted to be a black hole.[51][52]

Work by James Bardeen, Jacob Bekenstein, Carter, and Hawking in the early 1970s
led to the formulation of black hole thermodynamics.[53] 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.[54]

OBSERVATION

On 11 February 2016, the LIGO Scientific Collaboration and the Virgo
collaboration announced the first direct detection of gravitational waves,
representing the first observation of a black hole merger.[55] 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) in 2017 of the
supermassive black hole in Messier 87's galactic centre.[56][57][58] As of
2023[update], the nearest known body thought to be a black hole, Gaia BH1, is
around 1,560 light-years (480 parsecs) away.[59] Though only a couple dozen
black holes have been found so far in the Milky Way, there are thought to be
hundreds of millions, most of which are solitary and do not cause emission of
radiation.[60] Therefore, they would only be detectable by gravitational
lensing.

ETYMOLOGY

John Michell used the term "dark star" in a November 1783 letter to Henry
Cavendish[citation needed], 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.[61]

The term "black hole" was used in print by Life and Science News magazines in
1963,[61] 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.[62][63]

In December 1967, a student reportedly suggested the phrase "black hole" at a
lecture by John Wheeler;[62] Wheeler adopted the term for its brevity and
"advertising value", and it quickly caught on,[64] leading some to credit
Wheeler with coining the phrase.[65]

PROPERTIES AND STRUCTURE

The no-hair theorem postulates 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.
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.[47]

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 analogue of Gauss's law (through
the ADM mass), far away from the black hole.[66] Likewise, the angular momentum
(or spin) can be measured from far away using frame dragging by the
gravitomagnetic field, through for example the Lense–Thirring effect.[67]

An artistic depiction of a black hole and its features

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 behaviour 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.[68] 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.[69][70]

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 behaviour is so puzzling that it has been called
the black hole information loss paradox.[69][71]

PHYSICAL PROPERTIES

An animation of how light rays can be gravitationally bent

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.[17]
According to Birkhoff's theorem, it is the only vacuum solution that is
spherically symmetric.[72] 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.[73]

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.[74]

While the mass of a black hole can take any positive value, the charge and
angular momentum are constrained by the mass. The total electric charge Q and
the total angular momentum J are expected to 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. 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.[3] This is supported by
numerical simulations.[75]

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[76] appears to have an angular momentum near the maximum allowed value.
That uncharged limit is[77]

J ≤ G M 2 c , {\displaystyle J\leq {\frac {GM^{2}}{c}},}

allowing definition of a dimensionless spin parameter such that[77]

0 ≤ c J G M 2 ≤ 1. {\displaystyle 0\leq {\frac {cJ}{GM^{2}}}\leq 1.} [77][Note
1]

Black hole classifications Class Approx.
mass Approx.
radius Ultramassive black hole 109–1011 M☉ >1,000 AU Supermassive black hole
106–109 M☉ 0.001–400 AU Intermediate-mass black hole 102–105 M☉ 103 km ≈ REarth
Stellar black hole 2-150 M☉ 30 km Micro black hole up to MMoon up to 0.1 mm

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

r s = 2 G M c 2 ≈ 2.95 M M ⊙ k m , {\displaystyle r_{\mathrm {s} }={\frac
{2GM}{c^{2}}}\approx 2.95\,{\frac {M}{M_{\odot }}}~\mathrm {km,} }

where rs is the Schwarzschild radius and M☉ is the mass of the Sun.[79] 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[80]

r + = G M c 2 . {\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 centre
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.[82][83] 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.[84]

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.[85] 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.[86]

To a distant observer, clocks near a black hole would appear to tick more slowly
than those farther away from the black hole.[87] 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 amount of time to reach
it.[88] At the same time, all processes on this object slow down, from the
viewpoint of a fixed outside observer, causing any light emitted by the object
to appear redder and dimmer, an effect known as gravitational redshift.[89]
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.[90]

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.[91][92]

The topology of the event horizon of a black hole at equilibrium is always
spherical.[Note 4][95] 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.[96][97][98]

SINGULARITY

Main article: Gravitational singularity

At the centre of a black hole, as described by general relativity, may lie a
gravitational singularity, a region where the spacetime curvature becomes
infinite.[99] For a non-rotating black hole, this region takes the shape of a
single point; for a rotating black hole it is smeared out to form a ring
singularity that lies in the plane of rotation.[100] 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.[101] The singular region can thus be
thought of as having infinite density.[102]

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.[103] 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".[104]

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.[105] The
possibility of travelling to another universe is, however, only theoretical
since any perturbation would destroy this possibility.[106] 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.[107] It is expected that none of these peculiar effects
would survive in a proper quantum treatment of rotating and charged black
holes.[108]

The appearance of singularities in general relativity is commonly perceived as
signalling the breakdown of the theory.[109] 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.[110][111]

PHOTON SPHERE

Main article: Photon sphere

The photon sphere is a spherical boundary where photons that move on tangents to
that sphere would be trapped in a non-stable but circular orbit around the black
hole.[112] 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.[113]

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.[113] For a
Kerr black hole the radius of the photon sphere depends on the spin parameter
and on the details of the photon orbit, which can be prograde (the photon
rotates in the same sense of the black hole spin) or retrograde.[114][115]

ERGOSPHERE

Main article: Ergosphere
The ergosphere is a region outside of the event horizon, where objects cannot
remain in place.[116]

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.[117]

The ergosphere of a black hole is a volume bounded by the black hole's event
horizon and the ergosurface, which coincides with the event horizon at the poles
but is at a much greater distance around the equator.[116]

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 with. The extra energy is taken from the rotational energy of the
black hole. Thereby the rotation of the black hole slows down.[118] 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), for which any infinitesimal
inward perturbations to a circular orbit will lead to spiraling into the black
hole, and any outward perturbations will, depending on the energy, result in
spiraling in, stably orbiting between apastron and periastron, or escaping to
infinity.[119] The location of the ISCO depends on the spin of the black hole,
in the case of a Schwarzschild black hole (spin zero) is:

r I S C O = 3 r s = 6 G M c 2 , {\displaystyle r_{\rm {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.[120]

PLUNGING REGION

The final observable region of spacetime around a black hole is called the
plunging region. In this area it is no longer possible for matter to follow
circular orbits or to stop a final descent into the black hole. Instead it will
rapidly plunge toward the black hole close to the speed of light.[121][122]

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 stabilise their motion at some radius.[123] 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,[124] 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.[125]

Penrose demonstrated that once an event horizon forms, general relativity
without quantum mechanics requires that a singularity will form within.[48]
Shortly afterwards, Hawking showed that many cosmological solutions that
describe the Big Bang have singularities without scalar fields or other exotic
matter.[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.[126] 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.[127][128]

GRAVITATIONAL COLLAPSE

Main article: Gravitational collapse
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).[129]

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.[130]

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 if the outer layers have
been blown away (for example, in a Type II supernova). The mass of the remnant,
the collapsed object that survives the explosion, can be substantially less than
that of the original star. Remnants exceeding 5 M☉ are produced by stars that
were over 20 M☉ before the collapse.[130]

If the mass of the remnant exceeds about 3–4 M☉ (the Tolman–Oppenheimer–Volkoff
limit[26]), 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) is powerful enough to stop
the implosion and the object will inevitably collapse to form a black hole.[130]

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 centres of most galaxies.[131] It has
further been suggested that massive black holes with typical masses of ~105 M☉
could have formed from the direct collapse of gas clouds in the young
universe.[127] These massive objects have been proposed as the seeds that
eventually formed the earliest quasars observed already at redshift z ∼ 7
{\displaystyle z\sim 7} .[132] Some candidates for such objects have been found
in observations of the young universe.[127]

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.[133]

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 ( m P = ℏ
c / G {\displaystyle m_{P}={\sqrt {\hbar c/G}}} ≈ 1.2×1019 GeV/c2 ≈ 2.2×10−8 kg)
to hundreds of thousands of solar masses.[128]

Despite the early universe being extremely dense, it did not re-collapse into a
black hole during the Big Bang, since the expansion rate was greater than the
attraction. Following inflation theory there was a net repulsive gravitation in
the beginning until the end of inflation. Since then the Hubble flow was slowed
by the energy density of the universe.

Models for the 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.[134]

HIGH-ENERGY COLLISIONS

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.[135] 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, where quantum effects are expected to invalidate the
predictions of general relativity.[136]

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 minimum black hole mass could
be much lower: some braneworld scenarios for example put the boundary as low as
1 TeV/c2.[137] 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.[138] 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.[139]

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 growth process is one possible way through which some
supermassive black holes may have been formed, although the formation of
supermassive black holes is still an open field of research.[131] A similar
process has been suggested for the formation of intermediate-mass black holes
found in globular clusters.[140] 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.[131] The process has also
been proposed as the origin of some intermediate-mass black holes.[141][142]

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 ħc3/(8πGMkB);[54] 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.[143] 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.[54] 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.[144]

A stellar black hole of 1 M☉ has a Hawking temperature of 62 nanokelvins.[145]
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.[146] 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 millimetre.[147]

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 gravity 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.[148][149]

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.[150] NASA's Fermi Gamma-ray Space Telescope
launched in 2008 will continue the search for these flashes.[151]

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.[152] A
supermassive black hole with a mass of 1011 M☉ will evaporate in around 2×10100
years.[153] 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.[152]

OBSERVATIONAL EVIDENCE

By nature, black holes do not themselves emit any electromagnetic radiation
other than the hypothetical Hawking radiation, so astrophysicists searching for
black holes must generally rely on indirect observations. For example, a black
hole's existence can sometimes be inferred by observing its gravitational
influence on its surroundings.[154]

DIRECT INTERFEROMETRY

A view of M87* black hole in polarised light Sagittarius A*, black hole in the
center of the Milky Way

The Event Horizon Telescope (EHT) is an active program that directly observes
the immediate environment of black holes' event horizons, such as the black hole
at the centre of the Milky Way. In April 2017, EHT began observing the black
hole at the centre of Messier 87.[155][156] "In all, eight radio observatories
on six mountains and four continents observed the galaxy in Virgo on and off for
10 days in April 2017" to provide the data yielding the image in April
2019.[157]

After two years of data processing, EHT released the first direct image of a
black hole. Specifically, the supermassive black hole that lies in the centre of
the aforementioned galaxy.[158][159] What is visible is not the black hole—which
shows as black because of the loss of all light within this dark region.
Instead, it is the gases at the edge of the event horizon, displayed as orange
or red, that define the black hole.[160]

On 12 May 2022, the EHT released the first image of Sagittarius A*, the
supermassive black hole at the centre of the Milky Way galaxy. The published
image displayed the same ring-like structure and circular shadow as seen in the
M87* black hole, and the image was created using the same techniques as for the
M87 black hole. The imaging process for Sagittarius A*, which is more than a
thousand times smaller and less massive than M87*, was significantly more
complex because of the instability of its surroundings.[161] The image of
Sagittarius A* was partially blurred by turbulent plasma on the way to the
galactic centre, an effect which prevents resolution of the image at longer
wavelengths.[162]

The brightening of this material in the 'bottom' half of the processed EHT image
is thought to be caused by Doppler beaming, whereby material approaching the
viewer at relativistic speeds is perceived as brighter than material moving
away. In the case of a black hole, this phenomenon implies that the visible
material is rotating at relativistic speeds (>1,000 km/s [2,200,000 mph]), the
only speeds at which it is possible to centrifugally balance the immense
gravitational attraction of the singularity, and thereby remain in orbit above
the event horizon. This configuration of bright material implies that the EHT
observed M87* from a perspective catching the black hole's accretion disc nearly
edge-on, as the whole system rotated clockwise.[163][164]

The extreme gravitational lensing associated with black holes produces the
illusion of a perspective that sees the accretion disc from above. In reality,
most of the ring in the EHT image was created when the light emitted by the far
side of the accretion disc bent around the black hole's gravity well and
escaped, meaning that most of the possible perspectives on M87* can see the
entire disc, even that directly behind the "shadow".

In 2015, the EHT detected magnetic fields just outside the event horizon of
Sagittarius A* and even discerned some of their properties. The field lines that
pass through the accretion disc were a complex mixture of ordered and tangled.
Theoretical studies of black holes had predicted the existence of magnetic
fields.[165][166]

In April 2023, an image of the shadow of the Messier 87 black hole and the
related high-energy jet, viewed together for the first time, was
presented.[167][168]

DETECTION OF GRAVITATIONAL WAVES FROM MERGING BLACK HOLES

LIGO measurement of the gravitational waves at the Livingston (right) and
Hanford (left) detectors, compared with the theoretical predicted values

On 14 September 2015, the LIGO gravitational wave observatory made the
first-ever successful direct observation of gravitational waves.[55][169] The
signal was consistent with theoretical predictions for the gravitational waves
produced by the merger of two black holes: one with about 36 solar masses, and
the other around 29 solar masses.[55][170] This observation provides the most
concrete evidence for the existence of black holes to date. For instance, the
gravitational wave signal suggests that the separation of the two objects before
the merger was just 350 km, or roughly four times the Schwarzschild radius
corresponding to the inferred masses. The objects must therefore have been
extremely compact, leaving black holes as the most plausible interpretation.[55]

More importantly, the signal observed by LIGO also included the start of the
post-merger ringdown, the signal produced as the newly formed compact object
settles down to a stationary state. Arguably, the ringdown is the most direct
way of observing a black hole.[171] From the LIGO signal, it is possible to
extract the frequency and damping time of the dominant mode of the ringdown.
From these, it is possible to infer the mass and angular momentum of the final
object, which match independent predictions from numerical simulations of the
merger.[172] The frequency and decay time of the dominant mode are determined by
the geometry of the photon sphere. Hence, observation of this mode confirms the
presence of a photon sphere; however, it cannot exclude possible exotic
alternatives to black holes that are compact enough to have a photon
sphere.[171][173]

The observation also provides the first observational evidence for the existence
of stellar-mass black hole binaries. Furthermore, it is the first observational
evidence of stellar-mass black holes weighing 25 solar masses or more.[174]

Since then, many more gravitational wave events have been observed.[175]

STARS ORBITING SAGITTARIUS A*

Main article: Sagittarius A* cluster
Stars moving around Sagittarius A* as seen in 2021

The proper motions of stars near the centre of our own Milky Way provide strong
observational evidence that these stars are orbiting a supermassive black
hole.[176] Since 1995, astronomers have tracked the motions of 90 stars orbiting
an invisible object coincident with the radio source Sagittarius A*. By fitting
their motions to Keplerian orbits, the astronomers were able to infer, in 1998,
that a 2.6×106 M☉ object must be contained in a volume with a radius of 0.02
light-years to cause the motions of those stars.[177]

Since then, one of the stars—called S2—has completed a full orbit. From the
orbital data, astronomers were able to refine the calculations of the mass to
4.3×106 M☉ and a radius of less than 0.002 light-years for the object causing
the orbital motion of those stars.[176] The upper limit on the object's size is
still too large to test whether it is smaller than its Schwarzschild radius.
Nevertheless, these observations strongly suggest that the central object is a
supermassive black hole as there are no other plausible scenarios for confining
so much invisible mass into such a small volume.[177] Additionally, there is
some observational evidence that this object might possess an event horizon, a
feature unique to black holes.[178]

ACCRETION OF MATTER

See also: Accretion disk
Blurring of X-rays near black hole (NuSTAR; 12 August 2014)[179]

Due to conservation of angular momentum,[180] gas falling into the gravitational
well created by a massive object will typically form a disk-like structure
around the object. Artists' impressions such as the accompanying representation
of a black hole with corona commonly depict the black hole as if it were a
flat-space body hiding the part of the disk just behind it, but in reality
gravitational lensing would greatly distort the image of the accretion
disk.[181]

Within such a disk, friction would cause angular momentum to be transported
outward, allowing matter to fall farther inward, thus releasing potential energy
and increasing the temperature of the gas.[182]

When the accreting object is a neutron star or a black hole, the gas in the
inner accretion disk orbits at very high speeds because of its proximity to the
compact object. The resulting friction is so significant that it heats the inner
disk to temperatures at which it emits vast amounts of electromagnetic radiation
(mainly X-rays). These bright X-ray sources may be detected by telescopes. This
process of accretion is one of the most efficient energy-producing processes
known. Up to 40% of the rest mass of the accreted material can be emitted as
radiation.[182] In nuclear fusion only about 0.7% of the rest mass will be
emitted as energy. In many cases, accretion disks are accompanied by
relativistic jets that are emitted along the poles, which carry away much of the
energy. The mechanism for the creation of these jets is currently not well
understood, in part due to insufficient data.[183]

As such, many of the universe's more energetic phenomena have been attributed to
the accretion of matter on black holes. In particular, active galactic nuclei
and quasars are believed to be the accretion disks of supermassive black
holes.[184] Similarly, X-ray binaries are generally accepted to be binary star
systems in which one of the two stars is a compact object accreting matter from
its companion.[184] It has also been suggested that some ultraluminous X-ray
sources may be the accretion disks of intermediate-mass black holes.[185]

Stars have been observed to get torn apart by tidal forces in the immediate
vicinity of supermassive black holes in galaxy nuclei, in what is known as a
tidal disruption event (TDE). Some of the material from the disrupted star forms
an accretion disk around the black hole, which emits observable electromagnetic
radiation.

In November 2011 the first direct observation of a quasar accretion disk around
a supermassive black hole was reported.[186][187]

X-RAY BINARIES

See also: X-ray binary
A Chandra X-Ray Observatory image of Cygnus X-1, which was the first strong
black hole candidate discovered

X-ray binaries are binary star systems that emit a majority of their radiation
in the X-ray part of the spectrum. These X-ray emissions are generally thought
to result when one of the stars (compact object) accretes matter from another
(regular) star. The presence of an ordinary star in such a system provides an
opportunity for studying the central object and to determine if it might be a
black hole.[184]

If such a system emits signals that can be directly traced back to the compact
object, it cannot be a black hole. The absence of such a signal does, however,
not exclude the possibility that the compact object is a neutron star. By
studying the companion star it is often possible to obtain the orbital
parameters of the system and to obtain an estimate for the mass of the compact
object. If this is much larger than the Tolman–Oppenheimer–Volkoff limit (the
maximum mass a star can have without collapsing) then the object cannot be a
neutron star and is generally expected to be a black hole.[184]

The first strong candidate for a black hole, Cygnus X-1, was discovered in this
way by Charles Thomas Bolton,[188] Louise Webster, and Paul Murdin[189] in
1972.[190][191] Some doubt remained, due to the uncertainties that result from
the companion star being much heavier than the candidate black hole. Currently,
better candidates for black holes are found in a class of X-ray binaries called
soft X-ray transients. In this class of system, the companion star is of
relatively low mass allowing for more accurate estimates of the black hole mass.
These systems actively emit X-rays for only several months once every 10–50
years. During the period of low X-ray emission, called quiescence, the accretion
disk is extremely faint, allowing detailed observation of the companion star
during this period. One of the best such candidates is V404 Cygni.[184]

QUASI-PERIODIC OSCILLATIONS

Main article: Quasi-periodic oscillation

The X-ray emissions from accretion disks sometimes flicker at certain
frequencies. These signals are called quasi-periodic oscillations and are
thought to be caused by material moving along the inner edge of the accretion
disk (the innermost stable circular orbit). As such their frequency is linked to
the mass of the compact object. They can thus be used as an alternative way to
determine the mass of candidate black holes.[192]

GALACTIC NUCLEI

See also: Active galactic nucleus
Detection of unusually bright X-ray flare from Sagittarius A*, a black hole in
the centre of the Milky Way galaxy on 5 January 2015[193]

Astronomers use the term "active galaxy" to describe galaxies with unusual
characteristics, such as unusual spectral line emission and very strong radio
emission. Theoretical and observational studies have shown that the activity in
these active galactic nuclei (AGN) may be explained by the presence of
supermassive black holes, which can be millions of times more massive than
stellar ones. The models of these AGN consist of a central black hole that may
be millions or billions of times more massive than the Sun; a disk of
interstellar gas and dust called an accretion disk; and two jets perpendicular
to the accretion disk.[194][195]

Although supermassive black holes are expected to be found in most AGN, only
some galaxies' nuclei have been more carefully studied in attempts to both
identify and measure the actual masses of the central supermassive black hole
candidates. Some of the most notable galaxies with supermassive black hole
candidates include the Andromeda Galaxy, M32, M87, NGC 3115, NGC 3377, NGC 4258,
NGC 4889, NGC 1277, OJ 287, APM 08279+5255 and the Sombrero Galaxy.[196]

It is now widely accepted that the centre of nearly every galaxy, not just
active ones, contains a supermassive black hole.[197] The close observational
correlation between the mass of this hole and the velocity dispersion of the
host galaxy's bulge, known as the M–sigma relation, strongly suggests a
connection between the formation of the black hole and that of the galaxy
itself.[198]

MICROLENSING

Another way the black hole nature of an object may be tested is through
observation of effects caused by a strong gravitational field in their vicinity.
One such effect is gravitational lensing: The deformation of spacetime around a
massive object causes light rays to be deflected, such as light passing through
an optic lens. Observations have been made of weak gravitational lensing, in
which light rays are deflected by only a few arcseconds. Microlensing occurs
when the sources are unresolved and the observer sees a small brightening. The
turn of the millenium saw the first 3 candidate detections of black holes in
this way,[199][200] and in January 2022, astronomers reported the first
confirmed detection of a microlensing event from an isolated black hole.[201]

Another possibility for observing gravitational lensing by a black hole would be
to observe stars orbiting the black hole. There are several candidates for such
an observation in orbit around Sagittarius A*.[202]

ALTERNATIVES

SEE ALSO

* Black brane or Black string
* Black Hole Initiative
* Black hole starship
* Black holes in fiction
* Blanet
* BTZ black hole
* Golden binary
* Hypothetical black hole (disambiguation)
* Kugelblitz (astrophysics)
* List of black holes
* List of nearest black holes
* Outline of black holes
* Sonic black hole
* Virtual black hole
* Susskind-Hawking battle
* Timeline of black hole physics
* White hole
* Planck star
* Dark star (dark matter)

NOTES

1. ^ The value of cJ/GM2 can exceed 1 for objects other than black holes. The
largest value known for a neutron star is ≤ 0.4, and commonly used equations
of state would limit that value to < 0.7.[78]
2. ^ The (outer) event horizon radius scales as: M + M 2 − ( J / M ) 2 − Q 2 .
{\displaystyle M+{\sqrt {M^{2}-{(J/M)}^{2}-Q^{2}}}.}
3. ^ The set of possible paths, or more accurately the future light cone
containing all possible world lines (in this diagram the light cone is
represented by the V-shaped region bounded by arrows representing light ray
world lines), is tilted in this way in Eddington–Finkelstein coordinates
(the diagram is a "cartoon" version of an Eddington–Finkelstein coordinate
diagram), but in other coordinates the light cones are not tilted in this
way, for example in Schwarzschild coordinates they narrow without tilting as
one approaches the event horizon, and in Kruskal–Szekeres coordinates the
light cones do not change shape or orientation at all.[81]
4. ^ This is true only for four-dimensional spacetimes. In higher dimensions
more complicated horizon topologies like a black ring are possible.[93][94]
5. ^ In particular, he assumed that all matter satisfies the weak energy
condition.

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