While the vacuum and the scalar staticity theorems are based on differential identities and integration
by parts, the approach due to Sudarsky and Wald takes advantage of the ADM formalism and the existence
of a maximal slicing [84]. Along these lines, the authors of [302, 303
] were able to extend the staticity
theorem to topologically-trivial 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. This leaves some
room for stationary black holes, which are non-rotating and not static. Moreover, the theorem
implies that such configurations must be charged. On a perturbative level, the existence of
these charged, non-static black holes with vanishing total angular momentum was established
in [38
].
http://www.livingreviews.org/lrr-2012-7 |
Living Rev. Relativity 15, (2012), 7
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