General-relativistic kinetic theory of waves in a massive particle medium

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Abstract
In this paper, we give a general-relativistic kinetic theory of waves propagating in a medium filled with massive particles. A major difficulty of this problem is to handle simultaneously dispersive and expansion effects. Matter itself is at the root of both phenomena, and in our treatment they are conveniently separated by using a two-time scale approximation. It turns out that the expansion modifies both the amplitude and the frequency of the waves. Dispersion effects give rise to proper modes, which are shown to be the 0, 1, and 2 helicity components of the total field. The dispersion equations for these different components are obtained in a general form. The propagation of gravitational modes is examined in more detail for the two extreme cases of cold and ultrarelativistic matter. A lower cutoff frequency appears, and no Landau damping is found in the case of a thermalized gas.