$D=5$ Rotating Black Holes in Einstein-Gauss-Bonnet Gravity: Mass and Angular Momentum in Extremality

Abstract

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.

arXiv commentLatex, 32 pages, typos corrected, discussion expanded, version in JHEP

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