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.

Gauge-invariant gravitational waves in matter beyond linearized gravity

“…Understanding this coupling is potentially important, for example, for understanding the electromagnetic signatures of the GW radiation [5,6]. Also, since this coupling is small for the tensor modes and waves in cold matter [7], even small corrections due to thermal effects [8], viscosity [9], and matter-induced modification of the wave polarization [10,11] may be significant.…”

“…The tools for modeling dispersive GWs in matter can be imported from electrodynamics, plasma physics in particular, where the wave-induced oscillations of matter are commonly described in terms of electric susceptibility [12]. Provided that matter is continuously distributed in spacetime, its effect on a GW can be similarly, and conveniently, described in terms of gravitational susceptibility [11,13]. Then, by analogy with electrodynamics of continuous media [14], two questions arise: (i) How can one derive the equations of GW propagation at nonzero gravitational susceptibility of the ambient medium?…”

“…For small wave amplitudes, the first question can be answered within linear theory [11], but the second question cannot. The energy-momentum of a linear wave produces nonlinear average forces on the underlying medium, and is itself quadratic in the wave amplitude.…”

“…Here, we show how to do this using the tools that we have developed previously in [11,13,17,41,42]. Let us briefly describe this series of papers to put our work into perspective.…”

Torsional birefringence in metric-affine Chern-Simons gravity: gravitational waves in late-time cosmology

“…In particular, we speak of velocity birefringence when waves with left and right handed polarizations [59] propagate with different speeds, while in the presence of a different friction term for the two modes we have amplitude birefringence, in which the enhancement or suppression of the wave depends on its chiral state. Furthermore, when propagation within a material medium is also considered, it can be demonstrated that velocity birefringence can generate amplitude birefringence through the Landau damping phenomenon [60], consisting in the kinematic damping of gravitational waves in the absence of collisions (see [61][62][63][64][65][66][67][68][69][70][71][72] for more details). Gravitational wave birefringence is a well-established result of metric CSMG [23,[73][74][75], and in this work we show for the first time how such a phenomenon is present also in the metric-affine formulation.…”