Astrometric and Timing Effects of Gravitational Waves from Localized Sources

TL;DR

This paper develops an exact analytical framework within general relativity to analyze how gravitational waves from localized sources affect light propagation, including deflection and time delay, relevant for radio and gravitational wave observations.

Contribution

It provides a comprehensive solution for light propagation in the gravitational field of localized sources emitting quadrupolar gravitational waves, including explicit formulas and gauge conditions.

Findings

Exact integration of light propagation equations in gravitational wave fields.

Explicit expressions for light deflection and Shapiro delay.

Applicability to radio interferometry and gravitational wave data analysis.

Abstract

A consistent approach for an exhaustive solution of the problem of propagation of light rays in the field of gravitational waves emitted by a localized source of gravitational radiation is developed in the first post-Minkowskian and quadrupole approximation of General Relativity. We demonstrate that the equations of light propagation in the retarded gravitational field of an arbitrary localized source emitting quadrupolar gravitational waves can be integrated exactly. The influence of the gravitational field on the light propagation is examined not only in the wave zone but also in cases when light passes through the intermediate and near zones of the source. Explicit analytic expressions for light deflection and integrated time delay (Shapiro effect) are obtained accounting for all possible retardation effects and arbitrary relative locations of the source of gravitational waves, that of light rays, and the observer. It is shown that the ADM and harmonic gauge conditions can both be satisfied simultaneously outside the source of gravitational waves. Their use drastically simplifies the integration of light propagation equations and those for the motion of light source and observer in the 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 are elaborated in more detail. Explicit expressions for Shapiro effect and deflection angle are obtained in terms of the transverse-traceless part of the space-space components of the metric tensor. We also discuss the relevance of the developed formalism for interpretation of radio interferometric and timing observations, as well as for data processing algorithms for future gravitational wave detectors.