Indexed on: 21 Jul '20Published on: 12 Jul '20Published in: arXiv - General Relativity and Quantum Cosmology
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 have obtained 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 non-perturbative in mass has been 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.