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

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=<mml:mfrac>32</mml:mfrac>pi <mml:mfrac>13</mml:mfrac>J<mml:mfrac>23</mml:mfrac>+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.