Which gravitational lensing degeneracies are broken in wave-optics

This paper studies gravitational lensing degeneracies in the wave-optics regime, focusing on lensed gravitational waves (GWs). Considering lensing degeneracies as rescaling (or transformations) of arrival time delay surface, we can divide them into local and global types. Local degeneracies only affect the time delay surface in localized regions, whereas global degeneracies rescale the whole time delay surface by a constant while keeping the various observed image properties unchanged. We show that local degeneracies can be broken in the wave-optics regime since lensing effects become sensitive to the overall arrival time delay surface and not only to the time delay values at the image positions. On the other hand, global degeneracies (such as similarity transformation, prismatic transformation, and mass-sheet degeneracy) multiply the amplification factor by a constant factor (let us say, λ). However, in GW lensing, as the GW signal amplitude depends on the source distance, it turns out that λ is completely degenerate with the Hubble constant, similar to what we see in geometric optics. Hence, with the lensing of GWs, global degeneracies are as hard to break in wave optics as they are in geometric optics.