Black Holes and Causal Structure in Anti-de Sitter Isometric Spacetimes

TL;DR

This paper explores the causal structures of quotient spacetimes derived from anti-de Sitter space, revealing the existence of non-rotating black hole generalizations with unique properties in 2+1 and 3+1 dimensions.

Contribution

It characterizes the causal behavior of quotient anti-de Sitter spacetimes with one generator, including the discovery of a non-rotating, non-static black hole generalization in 3+1 dimensions.

Findings

No rotating BTZ-like black hole exists in 3+1 dimensions.

A non-rotating black hole with a non-trivial apparent horizon exists in 3+1 dimensions.

Causal structures depend on the quotient group properties.

Abstract

The observation that the 2+1 dimensional BTZ black hole can be obtained as a quotient space of anti-de Sitter space leads one to ask what causal behaviour other such quotient spaces can display. In this paper we answer this question in 2+1 and 3+1 dimensions when the identification group has one generator. Among other things we find that there does not exist any 3+1 generalization of the rotating BTZ hole. However, the non-rotating generalization exists and exhibits some unexpected properties. For example, it turns out to be non-static and to possess a non-trivial apparent horizon.