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We study static black hole solutions in Einstein and Einstein-Gauss-Bonnetgravity with product two-spheres topology, ${\bf SO(n) \times SO(n)}$, inhigher dimensions. There is an unusual new feature of Gauss-Bonnet black holethat the avoidance of non-central naked singularity prescribes a mass range forblack hole in terms of $\Lambda>0$. For Einstein-Gauss-Bonnet black hole alimited window of negative values for $\Lambda$ is also permitted. Thistopology encompasses black string and brane as well as a generalized Nariaimetric. We also give new solutions with product two-spheres of constantcurvatures.

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