More Nonlinearities? Electromagnetic and Gravitational Mode Mixing in NSBH Mergers

TL;DR

This paper explores how electromagnetic fields can influence gravitational wave signals in neutron star-black hole mergers, revealing nonlinear mode mixing effects and potential electromagnetic imprints on gravitational perturbations.

Contribution

It demonstrates electromagnetic and gravitational mode mixing in NSBH mergers using perturbation theory and simplified potential models, highlighting new nonlinear coupling phenomena.

Findings

Electromagnetic quasi normal modes can excite gravitational QNMs.

Linear and quadratic electromagnetic QNMs appear in gravitational perturbations.

Electromagnetic perturbations may induce polynomial tails in gravitational signals.

Abstract

We investigate the possibility of electromagnetic fields leaving imprints on gravitational wave (GW) signals from Neutron Star-Black hole (NSBH) mergers, specifically in the context of extreme mass ratio inspirals (EMRIs). Using black hole perturbation theory (BHPT) in the context of a minimally coupled Einstein-Maxwell system, we demonstrate that electromagnetic quasi normal modes(QNMs) can excite gravitational QNMs with frequencies that are linear or quadratic in the electromagnetic QNMs, at first level of mixing. Moreover, We then study the electromagnetism-gravity coupling by approximating the Regge-Wheeler and Zerilli potentials with Dirac delta functions. In this example, we examine gravitational perturbations induced by the electromagnetic field of an ideal dipole radially free fall towards the blackhole, building on calculations from a companion paper [1]. Our results show that both linear and quadratic electromagnetic QNMs appear in gravitational perturbations. In addition, linear gravitational QNMs are also excited due to the electromagnetic source, with their amplitudes depending on the details of the electromagnetic and gravitational potentials, analogous to gravitational mode mixing analysis. Furthermore, at late stages, gravitational perturbations might exhibit polynomial tails induced by electromagnetic perturbations. This article sets the stage for future numerical investigations aimed at identifying such modes in various scenarios.