Systematic Biases from the Gravitational Spin Hall Effect in Lensed Gravitational Waveforms

General relativity predicts gravitational waves are lensed when propagating near massive objects. In the infinite frequency limit, gravitational waves propagate along null geodesics of the spacetime. At high but finite frequencies, however, gravitational waves are perturbed from the null geodesic trajectories by a spin-orbit coupling known as the Gravitational Spin Hall Effect. The perturbed trajectories are frequency- and polarization-dependent, inducing a frequency-dependent time delay in observed waveforms. We investigate systematic parameter estimation errors arising from the spin-orbit coupling, and show the biases are well approximated by Taylor expanding the waveform about the best-fit parameters in the small-perturbation regime. We further discuss the detectability of such lensing effects relative to those in the infinite frequency limit.