Rotating Black Holes in Higher Dimensional Einstein-Maxwell Gravity

TL;DR

This paper presents new analytic solutions for rotating charged black holes in higher-dimensional Einstein-Maxwell gravity, extending known solutions to include multiple angular momenta and calculating their gyromagnetic ratios.

Contribution

It introduces a novel metric ansatz in N+1 dimensions and derives solutions describing slowly rotating charged black holes with one or two angular momenta.

Findings

Derived a solution for rotating charged black holes with a single angular momentum.

Provided the metric for black holes with two independent angular momenta in five dimensions.

Calculated the gyromagnetic ratio as g=N-1 for these black holes.

Abstract

The strategy of obtaining the familiar Kerr-Newman solution in general relativity is based on either using the metric ansatz in the Kerr-Schild form, or applying the method of complex coordinate transformation to a non-rotating charged black hole. In practice, this amounts to an appropriate re-scaling of the mass parameter in the metric of uncharged black holes. Using a similar approach, we assume a special metric ansatz in N+1 dimensions and present a new analytic solution to the Einstein-Maxwell system of equations. It describes rotating charged black holes with a single angular momentum in the limit of slow rotation. We also give the metric for a slowly rotating charged black hole with two independent angular momenta in five dimensions. We compute the gyromagnetic ratio of these black holes which corresponds to the value g=N-1.