AdS black hole explained

In theoretical physics, an anti-de Sitter (AdS) black hole is a black hole solution of general relativity or its extensions which represents an isolated massive object, but with a negative cosmological constant. Such a solution asymptotically approaches anti-de Sitter space at spatial infinity, and is a generalization of the Kerr vacuum solution, which asymptotically approaches Minkowski spacetime at spatial infinity.

In 3+1 dimensions, the metric is given by

ds ^{2} = - \left( k ^{2r} ^{2} + 1 - (C)/(r) \right)dt ^{2} + (1)/(k ^{2 r} ^{2} + 1 - (C)/(r)) dr ^{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 - (C)/(r ^{d-2}) \right)dt ^{2} + (1)/(k ^{2 r} ^{2} + 1 - (C)/(r ^{d-2})) dr ^{2} + r ^{2} d\Omega ^{2}

According to the AdS/CFT correspondence, 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, this would correspond to the deconfinement phase of the quark–gluon plasma.

See also

• BTZ black hole
• Black brane