A WKB FORMALISM FOR MULTICOMPONENT FIELDS AND ITS APPLICATION TO GRAVITATIONAL AND SOUND-WAVES IN PERFECT FLUIDS

We review the WKB method for multicomponent fields obeying hyperbolic linear partial differential equations and derive a general necessary a nd sufficient condition for the formalism to provide transport equatio ns. We apply the method to linearized perturbations of perfect fluid s olutions to Einstein's equation and show that the gravitational and so und wave modes satisfy this condition, whereas a zero-frequency, non-p ropagating matter mode does not. We derive the transport equations for the wave amplitudes in leading order; they exhibit in particular the influence of background curvature on the propagation of gravitational waves.