AdS black hole

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 $$d{s}^2=-(k^2{r}^2+1-\frac{C}{r})d{t}^2+\frac{1}{k^2{r}^2+1-\frac{C}{r}}d{r}^2+r^{2}d{\mathrm{\Omega }}^2$$ where Template:Mvar is the time coordinate, Template:Mvar is the radial coordinate, Ω are the polar coordinates, Template:Mvar is a constant and Template:Mvar is the AdS curvature.

In general, in d + 1 dimensions, the metric is given by $$d{s}^2=-(k^2{r}^2+1-\frac{C}{r^{d-2}})d{t}^2+\frac{1}{k^2{r}^2+1-\frac{C}{r^{d-2}}}d{r}^2+r^{2}d{\mathrm{\Omega }}^2$$

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

References

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