  This paper explores the hybridization of linear metric perturbations with
linear electromagnetic (EM) perturbations in non-magnetized plasma for a
general background metric. The local wave properties are derived from first
principles for inhomogeneous plasma, without assuming any symmetries of the
background metric. First, we derive the effective (``oscillation-center'')
Hamiltonian that governs the average dynamics of plasma particles in a
prescribed quasimonochromatic wave that involves metric perturbations and EM
fields simultaneously. Then, using this Hamiltonian, we derive the backreaction
of plasma particles on the wave itself and obtain gauge-invariant equations
that describe the resulting self-consistent gravito-electromagnetic (GEM) waves
in a plasma. The transverse tensor modes of gravitational waves are found to
have no interaction with the plasma and the EM modes in the geometrical-optics
limit. However, for ``longitudinal" GEM modes with large values of the
refraction index, the interplay between gravitational and EM interactions in
plasma can have a strong effect. In particular, the dispersion relation of the
Jeans mode is significantly affected by electrostatic interactions. As a
spin-off, our calculation also provides an alternative resolution of the
so-called Jeans swindle.
