We study the effect of the polarization of light beams on the time delay measured in Gravitational Wave experiments. To this end, we consider the Mathisson-Papapetrou-Dixon equations in a gravitational wave background, with two of the possible spin supplementary conditions: by Frenkel-Pirani, or by Tulczyjew. In the first case, photons follow a null geodesic and thus no spin effect is present. The second case shows a deviation of the photons from the null geodesic, resulting in a tiny effect on the measured time delay of photons depending on their polarization state.
Categories: gr-qc