Black holes with unusual topology

TL;DR

This paper explores black hole solutions in anti-de Sitter space with horizons of various topologies, including higher genus surfaces, revealing new parameters and properties that challenge traditional spherical assumptions.

Contribution

It introduces and analyzes black hole solutions with non-spherical topologies in anti-de Sitter space, detailing their parameters, thermodynamics, and stability.

Findings

Black holes with genus g horizons exist in anti-de Sitter space.

Higher genus black holes have additional free parameters, such as conformal class.

Mass spectrum of these black holes is positive definite.

Abstract

The Einstein's equations with a negative cosmological constant admit solutions which are asymptotically anti-de Sitter space. Matter fields in anti-de Sitter space can be in stable equilibrium even if the potential energy is unbounded from below, violating the weak energy condition. Hence there is no fundamental reason that black hole's horizons should have spherical topology. In anti-de Sitter space the Einstein's equations admit black hole solutions where the horizon can be a Riemann surface with genus $g$. The case $g=0$ is the asymptotically anti-de Sitter black hole first studied by Hawking-Page, which has spherical topology. The genus one black hole has a new free parameter entering the metric, the conformal class to which the torus belongs. The genus $g>1$ black hole has no other free parameters apart from the mass and the charge. All such black holes exhibits a natural temperature which is identified as the period of the Euclidean continuation and there is a mass formula connecting the mass with the surface gravity and the horizon area of the black hole. The Euclidean action and entropy are computed and used to argue that the mass spectrum of states is positive definite.