Uniqueness and non-uniqueness of static black holes in higher dimensions
Gary W. Gibbons, Daisuke Ida, Tetsuya Shiromizu
TL;DR
A uniqueness theorem for asymptotically flat static charged dilaton black-hole solutions in higher-dimensional space-times is proved and infinitely many nonasymptotical flat regular static black holes are constructed on the same space-time manifold with the same spherical topology.
Abstract
We prove a uniqueness theorem for asymptotically flat static charged dilaton black hole solutions in higher dimensional space-times. We also construct infinitely many non-asymptotically flat regular static black holes on the same space-time manifold with the same spherical topology. An application to the uniqueness of a certain class of flat $p$-branes is also given.