From the gates of the abyss: Frequency- and polarization-dependent lensing of gravitational waves in strong gravitational fields

Abstract:
The propagation of gravitational waves can be described in terms of null geodesics by using the geometrical optics approximation. However, at large but finite frequencies the propagation is affected by the spin-orbit coupling corrections to geometrical optics, known as the gravitational spin Hall effect. Consequently, gravitational waves follow slightly different frequency- and polarization-dependent trajectories. We study the potential for detection of the gravitational spin Hall effect in hierarchical triple black hole systems, consisting of an emitting binary orbiting a more massive body, acting as a gravitational lens. We calculate the difference in time of arrival with respect to the geodesic propagation and find that it follows a simple power law dependence on frequency with a fixed exponent. We calculate the gravitational spin Hall-corrected waveform and its mismatch with respect to the original waveform. The waveform carries a measurable imprint of the strong gravitational field if the source, lens and observer are sufficiently aligned or for generic observers if the source is close enough to the lens. We demonstrate that the gravitational spin Hall effect can be detected, providing an interesting avenue to probe general relativity and the environments of compact binary systems.

arXiv