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 [143Jump To The Next Citation Point] and Majumdar [128Jump To The Next Citation Point] 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 ChruĊ›ciel and Nadirashvili [42Jump To The Next Citation Point]; a complete proof is, however, not yet available (see also [90Jump To The Next Citation Point] for more information).

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