Cyclotron damping and Faraday rotation of gravitational waves

We study the propagation of gravitational waves in a collisionless plasma with an external magnetic field parallel to the direction of propagation. Due to resonant interaction with the plasma particles the gravitational wave experiences cyclotron damping or growth, the latter case being possible if the distribution function for any of the particle species deviates from thermodynamical equilibrium. Furthermore, we examine how the damping and dispersion depends on temperature and on the ratio between the cyclotron- and gravitational wave frequency. The presence of the magnetic field leads to different dispersion relations for different polarizations, which in turn imply Faraday rotation of gravitational waves.