The uniqueness theorem applies to the black hole solutions of Einstein’s vacuum equations
and the Einstein–Maxwell (EM) equations. Under certain conditions (see below), the
theorem implies that all stationary, asymptotically flat electrovac black hole space-times
(with non-degenerate horizon) are parametrized by the Kerr–Newman metric. The proof of
the theorem comprises various issues, not all of which have been settled in an equally reliable
manner.^{6}
The purpose of this section is to review the various steps involved in the classification of electrovac
space-times (see Figure 1). In the next section we shall then comment on the validity of the partial results
in the presence of non-linear matter fields.

2.1 Rigidity, staticity and circularity

2.2 The uniqueness theorems

2.3 Black holes with degenerate horizons

2.2 The uniqueness theorems

2.3 Black holes with degenerate horizons

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