Diffraction of gravitational waves by extended dark objects
Many dark sector models predict the formation of dark objects, such as solitons and dark stars, which can be searched for through their gravitational lensing of gravitational waves (GWs). Although these objects vary widely in size and compactness, most GW lensing studies have focused on point-like lenses. The finite size of an extended lens is important when it exceeds its Einstein radius. We evaluate the frequency-dependent effects on GW waveforms from extended lenses and demonstrate that they can be probed with current and future GW data. While finite-size effects can weaken the bounds on the fraction of dark matter in these objects compared to the point-like limit, current GW data provides complementary constraints to other gravitational tests for lens masses between $10^2M_\odot$ and $10^5M_\odot$; future LIGO-Virgo-KAGRA data and next-generation observatories will surpass their sensitivity. As expected, we find that the finite-size effects are important when the lens radius exceeds $\sim \text{few} \times 10^{6}R_\odot (M_L/100 M_\odot)^{1/2}$. Interpreting these constraints within specific models (a simple dissipative dark sector and axion stars), we show that current and future observations probe significant portions of the microphysical parameter space.