Nonlinear gravitational wave interactions with plasmas

We consider the interactions of a strong gravitational wave with electromagnetic fields using the 1+3 orthonormal tetrad formalism. A general system of equations is derived, describing the influence of a plane fronted parallel $\mathrm{}\left(\mathrm{pp}\right)\mathrm{}$ gravitational wave on a cold relativistic multicomponent plasma. We focus our attention on phenomena that are induced by terms that are higher order in the gravitational wave amplitude. In particular, it is shown that parametric excitations of plasma oscillations take place, due to higher order gravitational nonlinearities. The implications of the results are discussed.