Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary-moving and spinning bodies

The propagation of light in the gravitational field of self-gravitating spinning bodies moving with arbitrary velocities is discussed. The gravitational field is assumed to be weak everywhere. The equations of motion of a light ray are solved in the first post-Minkowskian approximation which is linear with respect to the universal gravitational constant G. We do not restrict ourselves to the approximation of a gravitational lens so that the solution of light geodesics is applicable for arbitrary locations of the source of light and the observer. This formalism is applied for studying corrections to the Shapiro time delay in binary pulsars caused by the rotation of the pulsar and its companion. We also derive the correction to the light deflection angle caused by the rotation of gravitating bodies in the solar system (Sun, planets) or a gravitational lens. The gravitational shift of frequency due to the combined translational and rotational motions of light-ray-deflecting bodies is analyzed as well. We give a general derivation of the formula describing the relativistic rotation of the plane of polarization of electromagnetic waves (Skrotskii effect). This formula is valid for arbitrary translational and rotational motion of gravitating bodies and greatly extends the results of previous researchers. Finally, we discuss the Skrotskii effect for gravitational waves emitted by localized sources such as a binary system. The theoretical results of this paper can be applied for studying various relativistic effects in microarcsecond space astrometry and developing corresponding algorithms for data processing in space astrometric missions such as FAME, SIM, and GAIA.