Light deflection by gravitational waves from localized sources

Abstract

We study the deflection of light (and the redshift, or integrated time delay) caused by the time-dependent gravitational field generated by a localized material source lying close to the line of sight. Our calculation explicitly takes into account the full, near-zone, plus intermediate-zone, plus wave-zone, retarded gravitational field. Contrary to several recent claims in the literature, we find that the deflections due to both the wave-zone $1/r$ gravitational wave and the intermediate-zone ${1/r}^{2}$ retarded fields vanish exactly. The leading total time-dependent deflection caused by a localized material source, such as a binary system, is proved to be given by the quasi-static, near-zone quadrupolar piece of the gravitational field, and therefore to fall off as the inverse cube of the impact parameter.