Black hole uniqueness theorems in higher dimensional spacetimes

TL;DR

This paper reviews key theorems and results concerning the uniqueness, topology, symmetries, and classification of higher-dimensional black hole spacetimes, highlighting proof ideas and potential generalizations.

Contribution

It provides a comprehensive overview of higher-dimensional black hole uniqueness theorems, including topology, symmetry, and supersymmetric classifications, with insights into proof strategies and extensions.

Findings

Theorems on the topology of higher-dimensional black holes.

Results on symmetries and rigidity of these spacetimes.

Classification of supersymmetric black holes.

Abstract

We review uniqueness theorems as well as other general results about higher dimensional black hole spacetimes. This includes in particular theorems about the topology of higher dimensional spacetimes, theorems about their symmetries (rigidity theorem), and the classification of supersymmetric black holes. We outline the basic ideas underlying the proofs of these statements, and we also indicate ways to generalize some of these results to more general contexts, such as more complicated theories.