Uniqueness and non-uniqueness of static vacuum black holes in higher dimensions

TL;DR

This paper proves a uniqueness theorem for asymptotically flat static vacuum black holes in higher dimensions and constructs numerous non-asymptotically flat static black holes with identical topology.

Contribution

It establishes the uniqueness of certain black hole solutions and introduces a method to construct many non-asymptotically flat solutions in higher dimensions.

Findings

Uniqueness theorem for asymptotically flat static vacuum black holes in higher dimensions.

Construction of infinitely many non-asymptotically flat static black holes.

Identification of conditions for black hole solution multiplicity.

Abstract

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.