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

Understand

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.