Novel way to the metric of higher dimensional 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.