Interaction between gravitational waves and plasma waves in the Vlasov description

The nonlinear interaction between electromagnetic, electrostatic and gravitational waves in a Vlasov plasma is reconsidered. By using a orthonormal tetrad description the three-wave coupling coefficients are computed. Comparing with previous results, it is found that the present theory leads to algebraic expression that are much reduced, as compared to those computed using a coordinate frame formalism. Furthermore, here we calculate the back-reaction on the gravitational waves, and a simple energy conservation law is deduced in the limit of a cold plasma.