Light rays, gravitational waves, and pulse-time offsets

One might expect light to be scattered when it passes through a gravitational wave, and might hope that in favourable circumstances these scatterings could be observed on Earth even if the interaction occurs far away. Damour and Esposito-Far\`ese, and Kopeikin, Sch\"afer, Gwinn and Eubanks, found that there were cancellations making such effects disappointingly small. Here I show that those cancellations depend on the emission of the light occurring far behind the gravity-wave source; for light-emissions near that source, larger effects are possible. I first develop a covariant treatment of the problem in exact general relativity (the propagation of light being modelled by geometric optics), and then specialise to linearised gravity. The most promising candidates identified here for detection in the not-too-distant future would involve sufficiently tight binaries as sources of gravitational radiation, and nearby pulsars as light-sources. In some favourable but not extreme cases, I find offsets in the pulses' times of arrival at Earth by ~ 10^{-10} -- 10^{-9} s, with periods half the binaries' periods.