High-frequency perturbations of coupled gravitational and electromagnetic fields in a weakly ionized dust

Abstract

Wavelike perturbations of a system consisting of a gravitational and an electromagnetic field and a dust with a small ionized component are studied. By using the spin coefficient formalism we expand the perturbations of the various quantities characterizing the system into asymptotic series. The whole dynamics of high-frequency waves is shown to be governed by four propagation equations for the expansion coefficients of the tetrad components\(\hat \psi _4\) and\(\hat \phi _2\) of perturbations of the Weyl tensor and Maxwell tensor in each order of the expansion. The perturbations of all the other variables can be derived without integration. The propagation equations are explicitly derived and discussed in the zeroth-order (geometrical optics) and in the first-order approximation. The influence of dust and plasma on the propagation is considered in the first-order equations.