Reinstating gauge invariance for gravitational-wave coupling to plasma

The recent observations of gravitational-wave (GW) bursts accompanied by electromagnetic (EM) radiation has revitalized the interest in the coupling between GWs and EM fields. However, a rigorous theory of this coupling is yet to be developed. In particular, reduced models of GWs in matter are typically contaminated with gauge artifacts. To fix this, we show how to find the gauge-invariant part of the metric perturbation in an arbitrary background metric (arXiv:2105.04680). We also propose a gauge-invariant adiabatic quasilinear theory and geometrical optics of dispersive GWs in matter (arXiv:2106.05062). We also show how gauge invariance can be maintained within a given accuracy if nonlinearities are included up to an arbitrary order in the GW amplitude.