While the vacuum and the scalar staticity theorems are based
on differential identities and Stokes' law, the new approach due
to Sudarsky and Wald takes advantage of the ADM formalism and a
maximal slicing property [43]. Along these lines, the authors of [167], [168] were also able to extend the staticity theorem to non-Abelian
black hole solutions. However, in contrast to the Abelian case,
the non-Abelian version applies only to configurations for which
either all components of the electric Yang-Mills charge or the
electric potential vanish asymptotically. As the asymptotic value
of a Lie algebra valued scalar is not a gauge freedom in the
non-Abelian case, the EYM staticity theorem leaves some room for
stationary black holes which are non-rotating - but not static.
Moreover, the theorem implies that these configurations must be
charged. On the perturbative level, the existence of these
charged, non-static black holes with vanishing total angular
momentum was recently established by rigorous means [21].
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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 |