Novel way to the metric of higher dimensional rotating black holes (2205.02231v2)

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.