AdS black hole

In theoretical physics, an AdS black hole is a black hole solution of general relativity or its extensions which represents an isolated massive object, but with a nonzero 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+1D, the metric is given by:$ds^2\; =\; -\; left(\; k^2r^2\; +\; 1\; -\; frac\{C\}\{r\}\; ight)dt^2\; +\; frac\{1\}\{k^2r^2\; +\; 1\; -\; frac\{C\}\{rdr^2\; +\; r^2\; dOmega^2$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+1D, the metric is given by:$ds^2\; =\; -\; left(\; k^2r^2\; +\; 1\; -\; frac\{C\}\{r^\{d-2\; ight)dt^2\; +\; frac\{1\}\{k^2r^2\; +\; 1\; -\; frac\{C\}\{r^\{d-2\}dr^2\; +\; r^2\; dOmega^2$

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.