Topological Black Holes in Anti-de Sitter Space

TL;DR

This paper explores black hole solutions in anti-de Sitter space with various horizon topologies, analyzing their thermodynamic properties and phase structure through the AdS/CFT correspondence.

Contribution

It introduces a class of topological black hole solutions in AdS space and examines their thermodynamics and phase behavior, extending previous models.

Findings

Calculated mass, temperature, and entropy of the solutions.

Identified phase transitions related to horizon topology.

Determined the mass dependence of Bekenstein-Hawking entropy.

Abstract

We consider a class of black hole solutions to Einstein's equations in d dimensions with a negative cosmological constant. These solutions have the property that the horizon is a (d-2)-dimensional Einstein manifold of positive, zero, or negative curvature. 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.