Gravitational wave modes in matter

TL;DR

This paper derives a gauge-invariant equation for dispersive gravitational waves in matter, revealing how matter influences GW modes, especially those strongly coupled with matter, and introduces a framework for GW interactions with plasmas.

Contribution

It presents a general linear gauge-invariant equation for dispersive GWs in matter, unifies tensor and matter-coupled modes, and extends GW theory to plasma interactions.

Findings

Matter effects on tensor modes are negligible in geometrical optics.

Identifies gravitational polarizability of matter and its role in GW behavior.

Reveals the kinetic Jeans instability as a collective GW mode.

Abstract

A general linear gauge-invariant equation for dispersive gravitational waves (GWs) propagating in matter is derived. This equation describes, on the same footing, both the usual tensor modes and the gravitational modes strongly coupled with matter. It is shown that the effect of matter on the former is comparable to diffraction and therefore negligible within the geometrical-optics approximation. However, this approximation is applicable to modes strongly coupled with matter due to their large refractive index. GWs in ideal gas are studied using the kinetic average-Lagrangian approach and the gravitational polarizability of matter that we have introduced earlier. In particular, we show that this formulation subsumes the kinetic Jeans instability as a collective GW mode with a peculiar polarization, which is derived from the dispersion matrix rather than assumed a priori. This forms a foundation for systematically extending GW theory to GW interactions with plasmas, where symmetry considerations alone are insufficient to predict the wave polarization.