Stationary Black Holes: Uniqueness and Beyond

TL;DR

This paper reviews recent developments in the classification of stationary black holes, highlighting the increasing diversity of solutions and the limitations of traditional uniqueness theorems in complex field theories.

Contribution

It discusses new findings that challenge the classical uniqueness theorems for black holes and explores the implications for understanding black-hole solutions in various theories.

Findings

Not all black-hole solutions are characterized solely by mass, charge, and angular momentum.

Symmetry properties of black-hole spacetimes vary in non-linear field theories.

Recent developments expand the known spectrum of stationary black-hole solutions.

Abstract

The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black-hole spacetimes ceases to exist in self-gravitating non-linear field theories. This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.