Propagation of light in the field of stationary and radiative gravitational multipoles

Abstract

Extremely high precision of near-future radio/optical interferometric observatories like SKA, Gaia, SIM and the unparalleled sensitivity of LIGO/LISA gravitational-wave detectors demands more deep theoretical treatment of relativistic effects in the propagation of electromagnetic signals through variable gravitational fields of the solar system, oscillating and precessing neutron stars, coalescing binary systems, exploding supernova and colliding galaxies. Especially important for future gravitational-wave observatories is the problem of the propagation of light rays in the field of multipolar gravitational waves emitted by a localized source of gravitational radiation. This paper suggests a physically-adequate and consistent solution of this problem in the first post-Minkowskian approximation of general relativity which accounts for all time-dependent multipole moments of an isolated astronomical system. We derive equations of propagation of electromagnetic wave in the retarded gravitational field of the localized source emitting gravitational waves of arbitrary multipolarity and integrate them analytically in closed form. We also prove that the leading terms in the observable relativistic effects (time delay, deflection angle and rotation of the plane of polarization of light) depend on the instantaneous value of the multipole moments of the isolated system and its time derivatives taken at the retarded instant of time but not on their integrated values. The influence of the multipolar gravitational field of the isolated system on the light propagation is examined for a general case when light propagates not only through the wave zone of the system but also through its intermediate and near zones. The gauge freedom of our formalism is carefully studied and all gauge-dependent terms are singled out and separated from observable quantities.