Parametric excitation of Alfvén waves by gravitational radiation

We consider the parametric excitation of Alfvén waves by gravitational radiation propagating on a Minkowski background, parallel to an external magnetic field. As a starting point, standard ideal magnetohydrodynamics equations incorporating the curvature of space-time has been derived. The growth rate of the Alfvén waves has been calculated, using the normal-mode approach. Various astrophysical applications of our investigations are discussed, and finally we demonstrate that the coupling coefficients of the interacting modes fulfill the Manley-Rowe relations.