A slightly different, rather powerful approach to stationary
space-times is obtained by taking advantage of their Kaluza-Klein
(KK) structure. As this approach is less commonly used in the
present context, we will discuss the KK reduction of the
Einstein-Hilbert(-Maxwell) action in some detail, (the more so
since this yields an efficient derivation of the Ernst equations
and the Mazur identity). Moreover, the inclusion of
non
-Abelian gauge fields within this framework [18] reveals a decisive structural difference between the
Einstein-Maxwell (EM) and the Einstein-Yang-Mills (EYM) system.
Before discussing the dimensional reduction of the field
equations in the presence of a Killing field, we start this
section by recalling the concept of the Killing horizon.
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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 |