Astrometric and timing effects of gravitational waves from localized sources - art. no. 084023

The extremely high precision of current radio interferometric observations demands a better theoretical treatment of secondary effects in the propagat ion of electromagnetic signals in variable gravitational fields. Such field s include those of oscillating and precessing stars, stationary or coalesci ng binary systems, and colliding galaxies. Especially important is the prob lem of propagation of light rays in the field of gravitational waves emitte d by a localized source of gravitational radiation. A consistent approach f or a complete and exhaustive solution of this problem is developed in the p resent paper in the first post-Minkowskian and quadrupole approximation of general relativity. This approximation is linear with respect to the univer sal gravitational constant G and accounts for the static monopole, spin, an d time-dependent quadrupole moments of an isolated system. We demonstrate f or the first time that the equations of light propagation in the retarded g ravitational field of an arbitrary localized source emitting quadrupole gra vitational waves can be integrated exactly in closed form. The influence of the gravitational field under consideration on the light propagation is ex amined not only in the wave zone but also in cases when light passes throug h the intermediate and near zones of the source. We reproduce the known res ults of integration of equations of light rays, both in a stationary gravit ational held and in the field of plane gravitational waves. establishing th e relationship between our new formalism and the simplified approaches of o ther authors. Explicit analytic expressions fur light deflection and integr ated time delay Shapiro effect are obtained accounting for all possible ret ardation effects and arbitrary relative locations of the source of gravitat ional waves, the source of light rays, and the observer. Coordinate depende nt terms in the expressions for observable quantities are singled out and u sed for physically meaningful interpretation of observable quantities. It i s shown that the ADM and harmonic gauge conditions can both be satisfied si multaneously outside the source of gravitational waves, Such ADM-harmonic c oordinates are extensively used in the present paper. Their use drastically simplifies the integration of light propagation equations and the equation s for the motion of light source and observer in the gravitational field of the source of gravitational waves, leading to the unique interpretation of observable effects. The two limiting cases of small and large values of impact parameter d are elaborated in more detail. It is proved that leading order terms for the ef fect of light deflection in thr case of small impact parameter depend neith er on the radiative part (similar to l/d) of the gravitational field nor on the intermediate (similar to l/d(2)) zone terms, confirming a previous res ult in the literature. The main effect rather comes from the near zone (sim ilar to l/d(3)) terms. This properly of strong suppression of the influence of gravitational waves on the propagation of light rays makes much more di fficult any direct detection of gravitational waves by VLBI or pulsar timin g techniques, in contrast with previous claims by other authors. We also pr esent a thorough-going analytical treatment of time delay anti bending of l ight in the case of large impact parameter. This exploration essentially ex tends previous results regarding propagation of light rays in the field of a plane monochromatic gravitational wave. Explicit expressions for Shapiro effect and deflection angle an obtained in terms of the transverse-traceles s (TT) part of the space-space components of the metric tensor. We also dis cuss the relevance of the developed formalism for interpretation of radio i nterferometric and timing observations, as well as for data processing algo rithms for future gravitational wave detectors. [S0556-2821(99)03706-6].