The purpose of this section is to estimate the generality of the various steps leading to the classification of electrovac black hole space-times. In particular, we shall argue that virtually all theorems displayed in Figure 1 cease to exist in the presence of non-Abelian gauge fields. Unfortunately, this implies that we are far from having a classification of all stationary black hole space-times.

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

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

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