A rotating black ring in five dimensions

TL;DR

This paper presents the first known vacuum solution in five-dimensional general relativity describing a rotating black ring with non-spherical topology, highlighting the complexity of higher-dimensional black hole solutions.

Contribution

It introduces a novel five-dimensional vacuum solution representing a rotating black ring with S^1 x S^2 topology, challenging four-dimensional uniqueness theorems.

Findings

Existence of two black ring solutions for certain mass and angular momentum ranges

Black rings can have arbitrarily large angular momentum for fixed mass

Transition from black hole to black ring occurs at high spin

Abstract

The vacuum Einstein equations in five dimensions are shown to admit a solution describing an asymptotically flat spacetime regular on and outside an event horizon of topology S^1 x S^2. It describes a rotating ``black ring''. This is the first example of an asymptotically flat vacuum solution with an event horizon of non-spherical topology. There is a range of values for the mass and angular momentum for which there exist two black ring solutions as well as a black hole solution. Therefore the uniqueness theorems valid in four dimensions do not have simple higher dimensional generalizations. It is suggested that increasing the spin of a five dimensional black hole beyond a critical value results in a transition to a black ring, which can have an arbitrarily large angular momentum for a given mass.