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
SU
(2) 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.