Doubly Spinning Black Rings

TL;DR

This paper develops a numerical method to analyze five-dimensional doubly spinning black rings with two angular momenta, providing insights into their properties and potential for higher-dimensional and cosmological constant extensions.

Contribution

It formulates a numerical approach for doubly spinning black rings, including perturbative solutions with backreaction, advancing the understanding of their physical properties.

Findings

Solutions are regular without conical singularities.

Phase diagram of entropy versus angular momenta is constructed.

Perturbative solutions include backreaction effects.

Abstract

We study a method to solve stationary axisymmetric vacuum Einstein equations numerically. As an illustration, the five-dimensional doubly spinning black rings that have two independent angular momenta are formulated in a way suitable for fully nonlinear numerical method. Expanding for small second angular velocity, the formulation is solved perturbatively upto second order involving the backreaction from the second spin. The obtained solutions are regular without conical singularity, and the physical properties are discussed with the phase diagram of the reduced entropy vs the reduced angular momenta. Possible extensions of the present approach to constructing the higher dimensional version of black ring and the ring with the cosmological constant are also discussed.