5 Beyond Einstein–Maxwell

The purpose of this section is to reexamine the various steps leading to the classification of electrovacuum black-hole spacetimes for other matter models. In particular, it will be seen that several steps in Figure 3View Image cease to hold in the presence of non-Abelian gauge fields. Unfortunately, this implies that we are far from having a classification of all stationary black-hole spacetimes with physically-interesting sources.

 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

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