
Abstract 
1 
Introduction 

1.1 
General 

1.2 
Organization 
2 
Classification of Stationary
Electrovac Black Hole SpaceTimes 

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
SpaceTimes 

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 SpaceTimes 

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 

References 

Footnotes 

Figures 