Topological Black Holes in Anti-de Sitter Space

A class of black hole solutions to Einstein’s equations in d dimensions with a negative cosmological constant is constructed. These solutions have the property that the horizon is a (d− 2)-dimensional manifold of constant curvature, but this curvature may be positive, zero, or negative. Asymptotically, the solutions are locally isometric to anti-de Sitter space. The mass, temperature, and entropy are calculated. Using the correspondence with conformal field theory, the phase structure of the solutions is examined, and used to determine the correct mass dependence of the Bekenstein-Hawking entropy.