Myers-Perry Black Hole in an External Gravitational Field

TL;DR

This paper presents a new exact 5D vacuum solution describing a distorted Myers-Perry black hole influenced by external matter, analyzing its physical properties, horizon geometry, and ergoregion, with implications for black hole angular momentum limits.

Contribution

The paper introduces a novel exact solution for a distorted Myers-Perry black hole using Bäcklund transformations, extending understanding of black hole properties in external gravitational fields.

Findings

Horizon angular momentum to mass ratio can be arbitrarily large.

External field distorts horizon geometry without changing topology.

Smarr-like relation holds for the distorted black hole.

Abstract

We obtain a new exact solution of the 5D Einstein equations in vacuum describing a distorted Myers-Perry black hole with a single angular momentum. Locally, the solution is interpreted as a black hole distorted by a stationary $U(1)\times U(1)$ symmetric distribution of external matter. Technically, the solution is constructed by applying a 2-fold B\"{a}cklund transformation on a 5D distorted Minkowski spacetime as a seed. The physical quantities of the solution are calculated, and a local Smarr-like relation on the black hole horizon is derived. It possesses the same form as the Smarr-like relation for the asymptotically flat Myers-Perry black hole. It is demonstrated that in contrast to the asymptotically flat Myers-Perry black hole, the ratio of the horizon angular momentum and the mass $J^2/ M^3$ is unbounded, and can grow arbitrarily large. We study the properties of the ergoregion and the horizon surface. The external field does not influence the horizon topology. The horizon geometry however is distorted, and any regular axisymmetric geometry is possible.