A black ring with a rotating 2-sphere

TL;DR

This work constructs a neutral black ring in five-dimensional vacuum gravity with rotation on the azimuthal direction of the $S^2$, controlled by three parameters and featuring a conical defect that prevents collapse. It analyzes the horizon geometry and global charges, establishing a Smarr relation and detailing the horizon area, temperature, and angular velocity. The paper further studies two important limits: an infinite-radius limit yielding the Kerr black string and a scaling limit leading to the Myers-Perry black hole with a single angular momentum, thereby linking the new solution to established spacetimes. Overall, it advances the understanding of high-dimensional black hole phase space and sets the stage for charged, multi-angular-momentum extensions and the pursuit of a broader class of non-supersymmetric black rings.

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.