Living Reviews in Relativity

"Stationary Black Holes: Uniqueness and Beyond"
Markus Heusler  

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1 Introduction
1.1 General
1.2 Organization
2 Classification of Stationary Electrovac Black Hole Space-Times
2.1 Rigidity, staticity and circularity
2.2 The uniqueness theorems
2.3 Black holes with degenerate horizons
3 Beyond Einstein–Maxwell
3.1 Spherically symmetric black holes with hair
3.2 Static black holes without spherical symmetry
3.3 The Birkhoff theorem
3.4 The staticity problem
3.5 Rotating black holes with hair
4 Stationary Space-Times
4.1 Killing horizons
4.2 Reduction of the Einstein–Hilbert action
4.3 The coset structure of vacuum gravity
4.4 Stationary gauge fields
4.5 The stationary Einstein–Maxwell system
5 Applications of the Coset Structure
5.1 The Mazur identity
5.2 Mass formulae
5.3 The Israel–Wilson class
6 Stationary and Axisymmetric Space-Times
6.1 Integrability properties of Killing fields
6.2 Boundary value formulation
6.3 The Ernst equations
6.4 The uniqueness theorem for the Kerr–Newman solution
7 Conclusion
8 Acknowledgments
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