Myers-Perry Black Hole in an External Gravitational Field

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 Bäcklund 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.

33 pages, 5 figures

References in corpus (8)

• Uniqueness theorem for 5-dimensional black holes with two axial Killing fields
• Solitonic generation of five-dimensional black ring solution
• Universal properties of distorted Kerr-Newman black holes
• 5D Einstein-Maxwell solitons and concentric rotating dipole black rings
• Interior of Distorted Black Holes
• Solitonic generation of vacuum solutions in five-dimensional General Relativity
• Rotating Black Holes on Kaluza-Klein Bubbles
• Distorted 5-dimensional vacuum black hole