D = 5 rotating black holes in Einstein-Gauss-Bonnet gravity: mass and angular momentum in extremality

Abstract

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 α. We obtain the near horizon structure of the near extremal solution, with the blackening factor of the order α. In the extremal limit, the mass-angular momentum relation reduces to $$ M=\frac{3}{2}{\pi}^{\frac{1}{3}}{J}^{\frac{2}{3}}+\pi \alpha $$ M = 3 2 π 1 3 J 2 3 + πα . The positive sign of the α-correction implies that the centrifugal repulsion associated with rotations becomes weaker than the gravitational attraction under the unitary requirement for the Gauss-Bonnet term.