Uniqueness and non-uniqueness of static vacuum black holes in higher   dimensions
  We prove the uniqueness theorem for asymptotically flat static vacuum black hole solutions in higher dimensional space-times. We also construct infinitely many non-asymptotically flat regular static black holes on the same spacetime manifold with the same spherical topology. 
Gary W. Gibbons, Daisuke Ida, Tetsuya Shiromizu