Quasi-normal modes for doubly rotating black holes

TL;DR

This paper derives the metric for doubly rotating higher-dimensional black holes, separates the Klein-Gordon equation, and develops numerical and perturbative methods to compute their quasi-normal modes for slow rotations.

Contribution

It provides explicit metric expressions, separates the Klein-Gordon equation, and introduces a numerical AIM approach along with perturbative expansions for doubly rotating black holes.

Findings

Derived explicit metrics for D≥6 doubly rotating black holes.

Separated Klein-Gordon equation into radial and angular parts.

Computed quasi-normal modes using AIM for slow rotations.

Abstract

Based on the work of Chen, L\"u and Pope, we derive expressions for the $D\geq 6$ dimensional metric for Kerr-(A)dS black holes with two independent rotation parameters and all others set equal to zero: $a_1\neq 0, a_2\neq0, a_3=a_4=...=0$. The Klein-Gordon equation is then explicitly separated on this background. For $D\geq 6$ this separation results in a radial equation coupled to two generalized spheroidal angular equations. We then develop a full numerical approach that utilizes the Asymptotic Iteration Method (AIM) to find radial Quasi-Normal Modes (QNMs) of doubly rotating flat Myers-Perry black holes for slow rotations. We also develop perturbative expansions for the angular quantum numbers in powers of the rotation parameters up to second order.