### 2.3 Black holes with degenerate horizons

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 ChruĊciel and Nadirashvili [42]; a complete proof is, however, not yet available (see also [90]
for more information).