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.Comment: 15 pages, 3 figures. Accepted for publication in Phys. Rev.
