Gravitational wave modes in matter
  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.
