General Relativistic Theory of Perturbations in a Perfect Fluid and the Possibility of Landau Damping of Gravitational Radiation.

Linear perturbation theory is applied to the problem of the modes in a perfect fluid as described by a self-consistent general relativistic theory and to the problem of Landau damping of gravitational radiation in a collisionless gas, also a self-consistent general relativistic analysis. A spatially flat Robertson Walker metric is used in the calculations. The treatment of fluid perturbations is done in a different gauge than previously published work. The treatment of Landau damping finds that gravitational waves in matter obey the same dispersion relation as light in a vacuum of similar space-time structure. The conclusions are that linear theory predicts only non-dispersive sound modes and vacuum-like gravitational waves in a perfect fluid. Landau damping is not possible due to the light-speed of gravitational waves.