theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

, an anti-de Sitter (AdS) black hole is a

black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...

solution of

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 ...

or its extensions which represents an isolated massive object, but with a negative cosmological constant. Such a solution asymptotically approaches

anti-de Sitter space In mathematics and physics, ''n''-dimensional anti-de Sitter space (AdS''n'') is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. Anti-de Sitter space and de Sitter space are named after Willem de Sitter (1872� ...

at spatial infinity, and is a generalization of the Kerr vacuum solution, which asymptotically approaches

Minkowski spacetime In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of Three-dimensional space, three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two Event (rel ...

at spatial infinity. In 3+1 dimensions, the metric is given by :

ds^2 = - \left( k^2r^2 + 1 - \frac \right)dt^2 + \fracdr^2 + r^2 d\Omega^2

where t is the time coordinate, r is the radial coordinate, Ω are the polar coordinates, C is a constant and k is the AdS curvature. In general, in d+1 dimensions, the metric is given by :

ds^2 = - \left( k^2r^2 + 1 - \frac \right)dt^2 + \fracdr^2 + r^2 d\Omega^2

According to the

AdS/CFT correspondence In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter s ...

, if gravity were quantized, an AdS black hole would be dual to a thermal state on the conformal boundary. In the context of say,

AdS/QCD In theoretical physics, the anti-de Sitter/quantum chromodynamics correspondence is a goal (not yet successfully accomplished) to describe quantum chromodynamics (QCD) in terms of a dual gravitational theory, following the principles of the AdS/C ...

, this would correspond to the

deconfinement In physics, deconfinement (in contrast to confinement) is a phase of matter in which certain particles are allowed to exist as free excitations, rather than only within bound states. Examples Various examples exist in particle physics where cert ...

phase of the

quark–gluon plasma Quark–gluon plasma (QGP) or quark soup is an interacting localized assembly of quarks and gluons at thermal (local kinetic) and (close to) chemical (abundance) equilibrium. The word ''plasma'' signals that free color charges are allowed. In a 1 ...

See also