Gravitational Waves in the Myers-Perry Geometry

TL;DR

This work addresses the separability of gravitational-wave perturbations in higher-dimensional rotating black holes of Myers–Perry and GLPP type by exploiting circle and sphere reductions with at least one vanishing rotation parameter. The authors formulate separable ansätze for vector and scalar modes, reducing the dynamics to Maxwell/Proca-type equations and wave equations for a separable master function $\Psi$, and derive explicit ODE systems in both odd and even dimensions. Key contributions include the demonstration of full separability for vector modes on partially rotated backgrounds, the introduction of generalized Proca equations on spheres, and the analysis of static limits and a hair-like perturbation example, providing analytic traction on GW dynamics in these spacetimes. The results extend the toolkit for analytic studies of higher-dimensional gravitational waves and lay groundwork for examining quasinormal spectra and stability in MP/GLPP geometries.

Abstract

We analyze equations describing gravitational waves in the Myers-Perry and Gibbons-Lu-Page-Pope geometries with arbitrary rotation parameters. Assuming that at least one rotation parameter vanishes, we demonstrate full separability of equations for several polarizations of gravitational waves and analyze the resulting ODEs. We also construct some examples of separable solutions describing gravitational excitations of black holes with the maximal number of rotation parameters.