Charged, rotating black holes in Einstein-Gauss-Bonnet gravity

Abstract

We consider the Einstein-Gauss-Bonnet equations in five dimensions including a negative cosmological constant and a Maxwell field. Using an appropriate Ansatz for the metric and for the electromagnetic fields, we construct numerically black holes with two equal angular momenta in the two orthogonal space-like planes of space-time. Families of such solutions, labeled by the angular momentum and by the electric charge are obtained for many representative intervals of the Gauss-Bonnet coupling constant $\alpha$. It is argued that, for fixed values of $\alpha$, the solutions terminate into extremal black holes at ($\alpha$-dependent) critical values of the angular momentum and/or of the electric charge. The influence of the Gauss-Bonnet coupling constant, of the charge and of the cosmological constant on the thermodynamics of the black holes and on their domain of existence is analyzed.