On static black holes solutions in Einstein and Einstein-Gauss-Bonnet gravity with topology Sⁿ x Sⁿ

We study static black hole solutions in Einstein and Einstein-Gauss-Bonnet gravity with the topology of the product of two spheres, Sⁿ x Sⁿ, in higher dimensions. There is an unusual new feature of the Gauss-Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of Λ > 0. For an Einstein-Gauss-Bonnet black hole a limited window of negative values for Λ is also permitted. This topology encompasses black strings, branes, and generalized Nariai metrics. We also give new solutions with the product of two spheres of constant curvature. (orig.)