Self-consistent interaction of linear gravitational and electromagnetic waves in non-magnetized plasma

TL;DR

This paper develops a self-consistent framework for analyzing the interaction between linear gravitational and electromagnetic waves in non-magnetized plasma, revealing significant effects on the dispersion of certain modes.

Contribution

It introduces a novel Hamiltonian approach to describe gravito-electromagnetic wave interactions in inhomogeneous plasma without symmetry assumptions.

Findings

Transverse gravitational waves do not interact with plasma or EM modes in the geometric optics limit.

Longitudinal GEM modes with high refraction index exhibit strong gravitational-electromagnetic interplay.

The dispersion relation of the Jeans mode is notably influenced by electrostatic interactions.

Abstract

This paper explores the hybridization of linear metric perturbations with linear electromagnetic (EM) perturbations in non-magnetized plasma for a general background metric. The local wave properties are derived from first principles for inhomogeneous plasma, without assuming any symmetries of the background metric. First, we derive the effective (``oscillation-center'') Hamiltonian that governs the average dynamics of plasma particles in a prescribed quasimonochromatic wave that involves metric perturbations and EM fields simultaneously. Then, using this Hamiltonian, we derive the backreaction of plasma particles on the wave itself and obtain gauge-invariant equations that describe the resulting self-consistent gravito-electromagnetic (GEM) waves in a plasma. The transverse tensor modes of gravitational waves are found to have no interaction with the plasma and the EM modes in the geometrical-optics limit. However, for ``longitudinal" GEM modes with large values of the refraction index, the interplay between gravitational and EM interactions in plasma can have a strong effect. In particular, the dispersion relation of the Jeans mode is significantly affected by electrostatic interactions. As a spin-off, our calculation also provides an alternative resolution of the so-called Jeans swindle.