A Double Myers-Perry Black Hole in Five Dimensions

TL;DR

This paper constructs an exact solution describing two rotating black holes in five dimensions, revealing insights into their interactions and singularities within a specific geometric background.

Contribution

It introduces a new six-parameter family of solutions for two Myers-Perry black holes in five dimensions using inverse scattering, simplifying previous models and enabling studies of spin interactions.

Findings

Solution describes superposition of two Myers-Perry black holes

Identifies conical and torsion singularities related to force and torque imbalance

Provides a simpler model for studying spin-spin interactions in 5D gravity

Abstract

Using the inverse scattering method we construct a six-parameter family of exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum Einstein equations, with U(1)^2 rotational symmetry. It describes the superposition of two Myers-Perry black holes, each with a single angular momentum parameter, both in the same plane. The black holes live in a background geometry which is the Euclidean C-metric with an extra flat time direction. This background possesses conical singularities in two adjacent compact regions, each corresponding to a set of fixed points of one of the U(1) actions in the Cartan sub-algebra of SO(4). We discuss several aspects of the black holes geometry, including the conical singularities arising from force imbalance, and the torsion singularity arising from torque imbalance. The double Myers-Perry solution presented herein is considerably simpler than the four dimensional double Kerr solution and might be of interest in studying spin-spin interactions in five dimensional general relativity.