Investigating strong lensing of gravitational waves by elliptical lensing potentials*

Massive objects distort spacetime, acting as gravitational lenses. Over a thousand galaxies and clusters have been observed as strong lenses, producing multiple or highly distorted, magnified images of distant electromagnetic (EM) sources. Lensing is a well-established tool with applications such as measuring the masses of distant galaxies and uncovering some of the earliest galaxies in the Universe. As detector sensitivity improves, detecting strong lensing of gravitational wave (GW) sources is becoming increasingly likely. For instance, the upcoming Laser Interferometer Space Antenna (LISA) will detect GWs from merging supermassive black holes at redshifts as high as z~10.

In strong GW lensing, the multiple images are magnified copies of the original GW signal. Since GWs have much lower frequencies than EM waves, the geometric-optics (GO) approximation breaks down in large parts of parameter space, depending on the lens mass. We investigate GW lensing by elliptical potentials, representing galaxy-scale lenses, and quantify where GO breaks down over the source plane. Where GO holds, we examine image time delays and GW event durations to determine whether multiple images will be detected separately or overlap. When images overlap, interference occurs, creating a distinctive modulation in the signal. Finally, we assess whether two-image templates suffice to identify more complex GW events.