Making Anti-de Sitter Black Holes

TL;DR

This paper extends the construction of black holes with event horizons from 2+1 to 3+1 dimensions in anti-de Sitter space, creating new topologies such as tori and higher genus surfaces while maintaining local anti-de Sitter geometry.

Contribution

It demonstrates the existence of higher-dimensional anti-de Sitter black holes with complex horizon topologies via point identifications, generalizing previous 2+1 dimensional results.

Findings

Black holes with toroidal and higher genus horizons are constructed.

These black holes have one or two asymptotic regions.

The local geometry remains isometric to anti-de Sitter space.

Abstract

It is known from the work of Banados et al. that a space-time with event horizons (much like the Schwarzschild black hole) can be obtained from 2+1 dimensional anti-de Sitter space through a suitable identification of points. We point out that this can be done in 3+1 dimensions as well. In this way we obtain black holes with event horizons that are tori or Riemann surfaces of genus higher than one. They can have either one or two asymptotic regions. Locally, the space-time is isometric to anti-de Sitter space.