This section reviews the structure of the stationary and axisymmetric field equations. We start by recalling the circularity problem (see also Sect. 2.1 and Sect. 3.5). It is argued that circularity is not a generic property of asymptotically flat, stationary and axisymmetric space-times. If, however, the symmetry conditions for the matter fields do imply circularity, then the reduction with respect to the second Killing field simplifies the field equations drastically. The systematic derivation of the Kerr-Newman metric and the proof of its uniqueness provide impressive illustrations of this fact.
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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 |