Speculative generalization of black hole uniqueness to higher dimensions

TL;DR

This paper discusses extending black hole uniqueness theorems to higher dimensions, highlighting failures in certain cases and proposing amendments involving horizon topology and stability considerations.

Contribution

It suggests modifications to the black hole uniqueness theorem for higher dimensions, emphasizing the importance of horizon topology and solution stability.

Findings

Uniqueness theorem fails for certain 5D black objects

Specifying horizon topology may restore uniqueness

Stability considerations could ensure theorem's validity

Abstract

A straightforward generalization of the celebrated uniqueness theorem to dimensions greater than four was recently found to fail in two pure gravity cases - the 5d rotating black ring and the black string on R^{3,1} * S^1. Two amendments are suggested here (without proof) in order to rectify the situation. The first is that in addition to specifying the mass and angular momentum (and gauge charges) one needs to specify the horizon topology as well. Secondly, the theorem may survive if applied exclusively to stable solutions. Note that the latter is at odds with the proposed stable but non-uniform string.