Scalar spheroidal harmonics in five dimensional Kerr-(A)dS

TL;DR

This paper derives the angular spheroidal harmonics for five-dimensional Kerr-(A)dS black holes, providing explicit solutions and perturbative expansions, which enhance understanding of wave equations in higher-dimensional rotating black hole spacetimes.

Contribution

It presents the first explicit separation of the Klein-Gordon equation in five-dimensional Kerr-(A)dS spacetime and provides perturbative eigenvalue expansions up to sixth order.

Findings

Derived the general five-dimensional Kerr-(A)dS metric.

Separated the Klein-Gordon equation explicitly.

Computed perturbative eigenvalues up to sixth order.

Abstract

We derive expressions for the general five-dimensional metric for Kerr-(A)dS black holes. The Klein-Gordon equation is explicitly separated and we show that the angular part of the wave equation leads to just one spheroidal wave equation, which is also that for charged five-dimensional Kerr-(A)dS black holes. We present results for the perturbative expansion of the angular eigenvalue in powers of the rotation parameters up to 6th order and compare numerically with the continued fraction method.