Speculative generalization of black hole uniqueness to higher dimensions

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.