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

Stationary Black Holes: Uniqueness and Beyond Markus Heusler http://www.livingreviews.org/lrr-1998-6 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de