Dynamics and gravitational interaction of waves in nonuniform media

We derive the generally covariant equations describing the propagation of waves with an arbitrary dispersion relation in a nonuniform, nondissipative medium. The back-reaction of the waves on the medium is expressed in terms of the wave energy-momentum tensor. The formalism is based on variations of the Lagrangian of the system with respect to the wave amplitude and phase and the particle orbits. The Lagrangian approach is considered in detail in the context of a cold, unmagnetized plasma. It is shown that the ''inertial'' mass of a photon in a plasma, namely the plasma frequency, is also its gravitational mass. Extremely precise experiments are needed to measure the gravitational ''free fall'' of phonons, plasmons, or photons in laboratory media. Finally, we indicate how the formalism can be extended to hot magnetized plasmas