Anti-de Sitter Quotients: When Are They Black Holes?

TL;DR

This paper refines the definition of BTZ black holes using anti-de Sitter space, clarifying their structure and addressing debates about their existence in higher dimensions.

Contribution

It provides a cleaner, more precise definition of BTZ black holes and resolves conflicting claims about their higher-dimensional counterparts.

Findings

Covering space can be taken as anti-de Sitter space

Scri splits into components due to Misner singularities

Clarifies the existence of BTZ black holes in 3+1 dimensions

Abstract

We point out that the BTZ black holes, and their relatives, can be defined in a cleaner way than they originally were. The covering space can be taken to be anti-de Sitter space, period, while scri splits up into components due to Misner singularities. Our definition permits us to choose between two conflicting claims concerning BTZ black holes in 3+1 dimensions.