Quasinormal modes for doubly rotating black holes

Abstract

Based on the work of Chen, L\"u, and Pope, we derive expressions for the $D\ensuremath{\ge}6$ dimensional metric for Kerr-anti-de Sitter black holes with two independent rotation parameters and all others set equal to zero: ${a}_{1}\ensuremath{\ne}0$, ${a}_{2}\ensuremath{\ne}0$, ${a}_{3}={a}_{4}=\ensuremath{\cdots}=0$. The Klein-Gordon equation is then explicitly separated on this background. For $D\ensuremath{\ge}6$ 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 to find radial quasinormal modes 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.