The uniqueness theorem outlined above applies exclusively to
Killing horizons with non-vanishing surface gravity. In fact, the
multi black hole solutions of Papapetrou [143] and Majumdar [128] illustrate that stationary EM black holes with degenerate
Killing horizons need not belong to the Kerr-Newman family. In
order to complete the classification of stationary electrovac
black hole space-times one has to include the Papapetrou-Majumdar
solutions, and to establish their uniqueness amongst the
stationary configurations with degenerate, non-connected
horizons. Some progress toward this goal was recently achieved by
Chrusciel and Nadirashvili [42]; a complete proof is, however, not yet available (see also [90] for more information).