Simply rotating higher dimensional black holes in Einstein-Gauss-Bonnet theory

TL;DR

This paper constructs rotating black hole solutions in higher-dimensional Einstein-Gauss-Bonnet gravity using perturbative methods, analyzing photon orbits to assess the solutions' properties and convergence.

Contribution

It provides the first perturbative rotating black hole solutions in Einstein-Gauss-Bonnet theory across arbitrary dimensions, including nonperturbative solutions in five dimensions.

Findings

Two solutions in 5D, one perturbative in mass.

Perturbative solutions up to order O(αa^3) in general D.

Nonperturbative 5D solution up to order O(αa^7).

Abstract

Using perturbative expansion in terms of powers of the rotation parameter $a$ we construct the axisymmetric and asymptotically flat black-hole metric in the $D$-dimensional Einstein-Gauss-Bonnet theory. In five-dimensional spacetime we find two solutions to the field equations, describing the asymptotically flat black holes, though only one of them is perturbative in mass, that is, goes over into the Minkowski spacetime when the black-hole mass goes to zero. We obtain the perturbative black-hole solution up to the order $O(\alpha a^3)$ for any $D$, where $\alpha$ is the Gauss-Bonnet coupling, while the $D=5$ solution which is nonperturbative in mass is found in analytic form up to the order $O(\alpha a^7)$. In order to check the convergence of the expansion in $a$ we analyze characteristics of photon orbits in this spacetime and compute frequencies of the photon orbits and radius of the photon sphere.