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A bstract 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=32^1{3}J^2{3}+ 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.
Ma et al. (Fri,) studied this question.