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, S-n x S-n, 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 Lambda > 0. For an Einstein-Gauss-Bonnet black hole a limited window of negative values for Lambda 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.