Novel way to the metric of higher dimensional rotating black holes

TL;DR

This paper extends a novel method for deriving rotating black hole metrics to higher dimensions, incorporating cosmological constants, and offers a new geometric approach to understanding such spacetimes.

Contribution

It generalizes a previous method for Kerr metrics to higher-dimensional rotating black holes with cosmological constant inclusion.

Findings

Derived higher-dimensional Myers-Perry black hole metrics

Included cosmological constant in the metric derivation

Provided a geometric framework for rotating black holes

Abstract

We wish to carry forward to higher dimensions the insightful and novel method of obtaining the Kerr metric proposed by one of us [Gen. Relativ. Gravit. 45, 2383 (2013)] for deriving the Myers-Perry rotating black hole metric. We begin with a flat spacetime metric written in oblate spheroidal coordinates (ellipsoidal geometry) appropriate for the inclusion of rotation, and then introduce arbitrary functions to introduce a gravitational potential due to mass, which are then determined by requiring that a massless particle experiences no acceleration, while a massive particle feels Newtonian acceleration at large r. We further generalize the method to include the cosmological constant {\Lambda} to obtain the MyersPerry de Sitter/antide Sitter black hole metric.