
Abstract 
1 
Introduction 

1.1 
General remarks 

1.2 
Organization 
2 
Definitions 

2.1 
Asymptotic
flatness 

2.2 
Kaluza–Klein asymptotic flatness 

2.3 
Stationary
metrics 

2.4 
Domains of outer communications, event horizons 

2.5 
Killing
horizons 

2.6 
I^{+}regularity 
3 
Towards a classification of stationary electrovacuum
black hole spacetimes 

3.1 
Static solutions 

3.2 
Stationaryaxisymmetric
solutions 

3.3 
The nohair theorem 

3.4 
Summary of open problems 
4 
Classification
of stationary toroidal Kaluza–Klein black holes 

4.1 
Black holes in higher
dimensions 

4.2 
Stationary toroidal Kaluza–Klein black holes 

4.3 
Topology
of the event horizon 

4.4 
Orbit space structure 

4.5 
KK topological
censorship 

4.6 
Classification theorems for KKblack holes 
5 
Beyond
Einstein–Maxwell 

5.1 
Spherically symmetric black holes with hair 

5.2 
Static
black holes without spherical symmetry 

5.3 
The Birkhoff theorem 

5.4 
The
staticity problem 

5.5 
Rotating black holes with hair 
6 
Stationary
Spacetimes 

6.1 
Reduction of the Einstein–Hilbert action 

6.2 
The coset
structure of vacuum gravity 

6.3 
Stationary gauge fields 

6.4 
The stationary
Einstein–Maxwell system 
7 
Some Applications 

7.1 
The Mazur identity 

7.2 
Mass
formulae 

7.3 
The Israel–Wilson–Perjés class 
8 
Stationary and Axisymmetric
Spacetimes 

8.1 
Integrability properties of Killing fields 

8.2 
Twodimensional
elliptic equations 

8.3 
The Ernst equations 

8.4 
The uniqueness theorem
for the Kerr–Newman solution 
9 
Acknowledgments 

References 

Footnotes 

Updates 

Figures 