Static electromagnetic Love tensors of 5-dimensional Myers-Perry black holes

TL;DR

This paper derives and analyzes static electromagnetic perturbation equations for five-dimensional Myers-Perry black holes, revealing exact solutions and the structure of tidal responses.

Contribution

It introduces a novel analysis of static electromagnetic perturbations, deriving exact solutions for certain modes and exploring the tidal Love tensor in higher-dimensional black holes.

Findings

Exact hypergeometric solutions for specific perturbation modes

Higher angular momentum modes are excited by lower angular momentum sources

The static tidal Love tensor can be computed iteratively

Abstract

We study the separable master equations for the electromagnetic and gravitational perturbations in five-dimensional Myers-Perry black holes. In the static limit, while the master equation for the electric polarization of the Maxwell field reduces to that of a massless scalar field, the magnetic polarization and gravitational perturbation yield Heun equations for both its angular and radial components. Remarkably, these Heun equations fall into a special class that admits exact analytic solutions in terms of hypergeometric functions. We reconstruct the gauge field using master fields and study its asymptotic behavior. When expanding the result in the basis of modified spherical harmonics, we find modes with higher angular momentum arise in response to the excitation of sources with lower angular momentum. The static tidal Love tensor that characterizes such mixing structure of the response can be computed iteratively. We also discuss the possible near zone approximation of the master equations for the magnetic polarization.