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.
The purpose of this section is to review the various steps
involved in the classification of electrovac space-times (see
Fig. 1). In the next section we shall then comment on the
validity of the partial results in the presence of non-linear
matter fields.
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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 |