# Stationary Black Holes: Uniqueness and Beyond

and

**João Lopes Costa**
Instituto Universitário de Lisboa (ISCTE-IUL), Lisboa, Portugal

Centro de Análise Matemática, Geometria e Sistemas Dinâmicos,

Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal

and

**Markus Heusler**
ITP, University of Zurich, CH-8057 Zurich

(at the time of writing original 1998 version)

###
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.