Light deflection by gravitational waves from localized sources

TL;DR

This paper analyzes light deflection caused by localized gravitational sources, demonstrating that dynamic gravitational wave contributions vanish and the main effect is a static quadrupolar field falling off as the inverse cube of the impact parameter.

Contribution

It provides a comprehensive calculation including all gravitational zones and refutes recent claims about non-vanishing wave-zone deflections.

Findings

Wave-zone gravitational wave deflections vanish exactly.

Main deflection is due to near-zone quadrupolar field.

Deflection falls off as the inverse cube of impact parameter.

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 proven 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.