Gravitational wave modes in matter

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.

Quasilinear theory for inhomogeneous plasma

“…(9.80) Equation (9.80) (where one takes p 0 = P 0 after the differentiation) is in agreement with the result that was obtained for quasimonochromatic waves in Garg & Dodin (2020). The derivation of the dispersion matrix Ξ for relativistic gravitational interactions in matter is cumbersome, so it is not presented here, but see Garg & Dodin (2022). The collision integral and fluctuations for relativistic gravitational interactions are straightforward to obtain from the general formulas presented in § § 6.9 and 8.…”