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D = 5 rotating black holes in Einstein-Gauss-Bonnet gravity: mass and angular momentum in extremality. (English) Zbl 1459.83043

Summary: We consider perturbative solutions in Einstein gravity with higher-derivative extensions and address some subtle issues of taking extremal limit. As a concrete new result, we construct the perturbative rotating black hole in five dimensions with equal angular momenta \(J\) and general mass \(M\) in Einstein-Gauss-Bonnet gravity, up to and including the linear order of the standard Gauss-Bonnet coupling constant \(\alpha\). We obtain the near horizon structure of the near extremal solution, with the blackening factor of the order \(\alpha\). In the extremal limit, the mass-angular momentum relation reduces to \(M=\frac{3}{2}{\pi}^{\frac{1}{3}}{J}^{\frac{2}{3}}+\pi \alpha\). The positive sign of the \(\alpha\)-correction implies that the centrifugal repulsion associated with rotations becomes weaker than the gravitational attraction under the unitary requirement for the Gauss-Bonnet term.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C15 Exact solutions to problems in general relativity and gravitational theory
83C57 Black holes
83C40 Gravitational energy and conservation laws; groups of motions
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