Lensing of Gravitational Wave Sources by Elliptical Potentials

Strong gravitational lensing of electromagnetic (EM) sources is well established as a crucial tool in astrophysics, with applications such as investigating dark matter, and studying the most distant galaxies in the Universe. Although strong lensing of gravitational wave (GW) sources has not yet been detected for LIGO-Virgo-KAGRA events, detection will become increasingly likely with the increasing sensitivity of current and future ground-based and future space-based detectors. A key difference between EM and GW lensing is the validity of the geometrical-optics (GO) approximation, which breaks down over much of GW lensing parameter space depending on the mass of the lens. We study the GW lensing properties of elliptical potentials, good representations of galaxy-scale lenses, using the quasi-geometric optics approximation to quantify the breakdown of the GO approximation. Our focus is on the regime where the time delay between multiple images (magnified versions of GW signals) is much smaller than the GW event duration. In this regime, images overlap at a GW detector, and interference occurs. We compute the mismatches between lensed GW signals with two or four images and establish whether two-image templates will suffice for the identification of more complex GW events.