Rotating Black Hole
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A rotating black hole is a
black hole A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can defo ...
that possesses
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed sy ...
. In particular, it rotates about one of its axes of symmetry. All celestial objects –
planets A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a young ...
, stars ( Sun), galaxies, black holes – spin.


Types of black holes

There are four known, exact, black hole solutions to the
Einstein field equations In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form ...
, which describe gravity in
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. ...
. Two of those rotate: the Kerr and Kerr–Newman black holes. It is generally believed that every black hole decays rapidly to a stable black hole; and, by the
no-hair theorem The no-hair theorem states that all stationary black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three independent ''externally'' observab ...
, that (except for quantum fluctuations) stable black holes can be completely described at any moment in time by these 11 numbers: * mass-energy ''M'', * linear momentum ''P'' (three components), *
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed sy ...
''J'' (three components), *
position Position often refers to: * Position (geometry), the spatial location (rather than orientation) of an entity * Position, a job or occupation Position may also refer to: Games and recreation * Position (poker), location relative to the dealer * ...
''X'' (three components), *
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respecti ...
''Q''. These numbers represent the conserved attributes of an object which can be determined from a distance by examining its electromagnetic and gravitational fields. All other variations in the black hole will either escape to infinity or be swallowed up by the black hole. This is because anything happening inside the black hole horizon cannot affect events outside of it. In terms of these properties, the four types of black holes can be defined as follows: Note that astrophysical black holes are expected to have non-zero angular momentum, due to their formation via collapse of rotating stellar objects, but effectively zero charge, since any net charge will quickly attract the opposite charge and neutralize. For this reason the term "astrophysical" black hole is usually reserved for the Kerr black hole.


Formation

Rotating black holes are formed in the
gravitational collapse Gravitational collapse is the contraction of an astronomical object due to the influence of its own gravity, which tends to draw matter inward toward the center of gravity. Gravitational collapse is a fundamental mechanism for structure formatio ...
of a massive spinning
star A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth make ...
or from the collapse or collision of a collection of compact objects, stars, or gas with a total non-zero angular momentum. As all known stars
rotate Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
and realistic collisions have non-zero angular momentum, it is expected that all black holes in nature are rotating black holes. Since observed astronomical objects do not possess an appreciable net electric charge, only the Kerr solution has astrophysical relevance. In late 2006, astronomers reported estimates of the spin rates of black holes in ''
The Astrophysical Journal ''The Astrophysical Journal'', often abbreviated ''ApJ'' (pronounced "ap jay") in references and speech, is a peer-reviewed scientific journal of astrophysics and astronomy, established in 1895 by American astronomers George Ellery Hale and Ja ...
''. A black hole in the Milky Way, GRS 1915+105, may rotate 1,150 times per second, approaching the theoretical upper limit.


Relation with gamma ray bursts

The formation of a rotating black hole by a
collapsar A collapsar is a star which has undergone gravitational collapse. When a star no longer has enough fuel for significant fusion reactions, there are three possible outcomes, depending on the star's mass: If it is less than the Chandrasekhar limit ...
is thought to be observed as the emission of gamma ray bursts.


Conversion to a Schwarzschild black hole

A rotating black hole can produce large amounts of energy at the expense of its rotational energy. This happens through the Penrose process in the black hole's ergosphere, an area just outside its event horizon. In that case a rotating black hole gradually reduces to a Schwarzschild black hole, the minimum configuration from which no further energy can be extracted, although the Kerr black hole's rotation velocity will never quite reach zero.


Kerr metric, Kerr–Newman metric

A rotating black hole is a solution of
Einstein's field equation In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the fo ...
. There are two known exact solutions, the
Kerr metric The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of ...
and the Kerr–Newman metric, which are believed to be representative of all rotating black hole solutions, in the exterior region. In the vicinity of a black hole, space curves so much that light rays are deflected, and very nearby light can be deflected so much that it travels several times around the black hole. Hence, when we observe a distant background galaxy (or some other celestial body), we may be lucky to see the same image of the galaxy multiple times, albeit more and more distorted. A complete mathematical description for how light bends around the equatorial plane a Kerr black hole was published in 2021. In 2022, it was mathematically demonstrated that the equilibrium found by Kerr in 1963 was stable and thus black holes—which were the solution to Einstein's equation of 1915—were stable.


State transition

Rotating black holes have two temperature states they can exist in: heating (losing energy) and cooling. In 1989,
Paul Davies Paul Charles William Davies (born 22 April 1946) is an English physicist, writer and broadcaster, a professor in Arizona State University and Director of BEYOND: Center for Fundamental Concepts in Science. He is affiliated with the Institu ...
argued that the transition between the two states occurs when the square of the black hole's mass-to-angular-momentum ratio, in Planck units, equals the
golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( ...
. This claim was later found to be incorrect and in contradiction with Davies' earlier work.


In popular culture

Kerr black holes are featured extensively in the 2009
visual novel A , often abbreviated as VN, is a form of digital semi-interactive fiction. Visual novels are often associated with and used in the medium of video games, but are not always labeled as such themselves. They combine a textual narrative with sta ...
Steins;Gate ''Steins;Gate'' is a 2009 science fiction visual novel game developed by 5pb. and Nitroplus. It is the second game in the ''Science Adventure'' series, following ''Chaos;Head''. The story follows a group of students as they discover and develo ...
(also TV /
manga Manga ( Japanese: 漫画 ) are comics or graphic novels originating from Japan. Most manga conform to a style developed in Japan in the late 19th century, and the form has a long prehistory in earlier Japanese art. The term ''manga'' is use ...
), for their possibilities in time travelling. These are, however, magnified greatly for the purpose of story telling. Kerr black holes are also key to the "Swan Song" project by Joe Davis (artist).


See also

* Black hole bomb * Black hole spin parameter * Black hole spin-flip * BKL singularity – solution representing interior geometry of black holes formed by gravitational collapse. * Ergosphere * Kerr black holes as wormholes * Penrose process * Ring singularity * Stellar black holes


References


Further reading

* * * * {{Black holes Black holes
Black hole A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can defo ...