The fact that the stationary electrovac black holes are parametrized by their mass, angular momentum and electric charge is due to the distinguished structure of the Einstein–Maxwell equations in the presence of a Killing symmetry. In general, the classification of the stationary black hole space-times within a given matter model is a difficult task, involving the investigation of Einstein’s equations with a low degree of symmetries. The variety of black hole configurations in the Einstein–Yang–Mills system indicates that – in spite of its beautiful and intuitive content – the uniqueness theorem is a distinguished feature of electrovac space-times. In general, the stationary black hole solutions of self-gravitating matter fields are considerably less simple than one might have expected from the experience with the Einstein–Maxwell system.
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