A black ring with a rotating 2-sphere

TL;DR

This paper presents a five-dimensional vacuum solution describing a rotating black ring with horizon topology S^1 x S^2, connecting known black hole solutions and highlighting the effects of conical singularities.

Contribution

It introduces a new exact solution for a rotating black ring in five dimensions, demonstrating its relation to known black hole solutions and analyzing its horizon properties.

Findings

Reproduces Kerr black string in the infinite radius limit.

Recovers Myers-Perry black hole with a single angular momentum.

Identifies conical singularities related to unbalanced rotation.

Abstract

We present a solution of the vacuum Einstein's equations in five dimensions corresponding to a black ring with horizon topology S^1 x S^2 and rotation in the azimuthal direction of the S^2. This solution has a regular horizon up to a conical singularity, which can be placed either inside the ring or at infinity. This singularity arises due to the fact that this black ring is not balanced. In the infinite radius limit we correctly reproduce the Kerr black string, and taking another limit we recover the Myers-Perry black hole with a single angular momentum.