Coupling between gravitational and electromagnetic perturbations on Kerr Spacetime

TL;DR

This paper develops a framework for analyzing gravitational-electromagnetic coupling in rotating black holes using Kerr spacetime, deriving source terms for the Teukolsky equation, and exploring implications for astrophysical observations and fundamental physics.

Contribution

It extends previous Schwarzschild-based studies to Kerr spacetime, deriving explicit source terms for the Teukolsky equation and analyzing the potential observational relevance of quadratic quasinormal modes.

Findings

GEM quadratic quasinormal modes can be relevant in astrophysical scenarios.

The GEM spectrum is sensitive to how gravity couples to electromagnetism.

Provides a foundation for future numerical and observational studies of black-hole spectroscopy.

Abstract

We extend our previous Schwarzschild metric-based studies of gravitational--electromagnetic (GEM) coupling to rotating black holes by working directly in a curvature-based Newman--Penrose/Teukolsky framework on Kerr spacetime. Within a minimally coupled Einstein--Maxwell system, we derive explicit quadratic electromagnetic source terms for the spin-$-2$ Teukolsky equation, providing a foundation for future numerical studies of GEM interactions in the framework of black-hole spectroscopy. Moreover, we give order-of-magnitude arguments showing that GEM quadratic quasinormal modes (QQNMs) can become relevant in a range of charged and magnetized astrophysical scenarios. Finally, we show through a brief dilaton-theory example that the GEM QQNM spectrum is sensitive to how gravity couples to electromagnetism, thereby providing a model-based way to test minimal coupling and to constrain hidden $U(1)$ sectors with gravitational-wave observations.