On static black holes solutions in Einstein and Einstein-Gauss-Bonnet gravity with topology ${\bf SO(n) \times SO(n)}$

TL;DR

This paper explores static black hole solutions with ${\bf SO(n) \times SO(n)}$ topology in higher-dimensional Einstein and Einstein-Gauss-Bonnet gravity, revealing unique features like mass constraints and new solutions with constant curvature two-spheres.

Contribution

It introduces novel static black hole solutions with product two-spheres topology, highlighting unique features in Einstein-Gauss-Bonnet gravity and expanding the understanding of higher-dimensional black holes.

Findings

Gauss-Bonnet black holes avoid non-central naked singularities within a specific mass range.

Limited negative cosmological constant window is permitted for Einstein-Gauss-Bonnet black holes.

New solutions with constant curvature product two-spheres are presented.

Abstract

We study static black hole solutions in Einstein and Einstein-Gauss-Bonnet gravity with product two-spheres topology, ${\bf SO(n) \times SO(n)}$, in higher dimensions. There is an unusual new feature of Gauss-Bonnet black hole that the avoidance of non-central naked singularity prescribes a mass range for black hole in terms of $\Lambda>0$. For Einstein-Gauss-Bonnet black hole a limited window of negative values for $\Lambda$ is also permitted. This topology encompasses black string and brane as well as a generalized Nariai metric. We also give new solutions with product two-spheres of constant curvatures.