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

TL;DR

This paper constructs a perturbative five-dimensional rotating black hole solution in Einstein-Gauss-Bonnet gravity, analyzing its near horizon structure and extremal limit, revealing how higher-derivative corrections affect mass and angular momentum relations.

Contribution

It provides the first perturbative rotating black hole solution in five dimensions with Gauss-Bonnet corrections, including the extremal limit and near horizon analysis.

Findings

Mass-angular momentum relation includes Gauss-Bonnet correction: M = (3/2)π^{1/3} J^{2/3} + π α.

Positive α correction weakens centrifugal repulsion compared to gravity.

Near horizon structure of near extremal solutions characterized by blackening factor of order α.

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 $M=\frac32 \pi^{\frac13} J^{\frac23} + \pi \alpha$. 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.