Gravitational ponderomotive forces and linear gravitational waves in matter

Recent detection of electromagnetic waves accompanying gravitational-wave (GW) emission by astrophysical sources has reinvigorated interest in the problem of GW coupling with plasma surrounding the sources. Existing theories of such coupling are cumbersome and not directly applicable to the GWs of interest that are inhomogeneous in space and have more general polarization than in vacuum. We propose an alternative, variational formulation of this problem, which also leads to the prediction of the nonlinear ponderomotive force that a GW pulse exerts on massive particles. This force is calculated explicitly for the first time. Developing on our variational method, we also propose a geometrical-optics theory for collective matter oscillations in self-consistent metric with general polarization. Electromagnetic interactions can be added similarly, leading to a generalized theory of plasma waves in astrophysical context.