Nonlinear coupled Alfv\'{e}n and gravitational waves

TL;DR

This paper models the nonlinear interaction between gravitational and electromagnetic waves in a magnetized plasma, deriving a wave equation and discussing potential observational effects like electromagnetic focusing from pulsar mergers.

Contribution

It presents a self-consistent weakly nonlinear analysis of Einstein-Maxwell equations, deriving a nonlinear Schrödinger equation for coupled wave modes in a plasma.

Findings

Electromagnetic radiation may be focused during pulsar binary mergers.

Derived wave equation describes nonlinear coupling of gravitational and electromagnetic waves.

Potential detectability of electromagnetic focusing effects in astrophysical events.

Abstract

In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation perpendicular to a background magnetic field, and the coupling to compressional Alfv\'{e}n waves. The gravitational waves are considered in the high frequency limit and the plasma is modelled by a multifluid description. We make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell system and derive a wave equation for the coupled gravitational and electromagnetic wave modes. A WKB-approximation is then applied and as a result we obtain the nonlinear Schr\"{o}dinger equation for the slowly varying wave amplitudes. The analysis is extended to 3D wave pulses, and we discuss the applications to radiation generated from pulsar binary mergers. It turns out that the electromagnetic radiation from a binary merger should experience a focusing effect, that in principle could be detected.