Associating fast radio bursts with compact binary mergers via gravitational lensing

The origin of fast radio bursts (FRBs) is currently an open question with several proposed sources and corresponding mechanisms for their production. Among them are compact binary coalescences (CBCs) that also generate gravitational waves (GWs). Spatial and temporal coincidences between GWs and FRBs have so far been used to search for potential FRB counterparts to GWs from CBCs. However, such methods suffer from relatively poor sky-localisation of the GW sources, and similarly poor luminosity distance estimates of both GW and FRB sources. The expected time delay between the GW and radio emission is also poorly understood. In this work, we propose an astrophysical scenario that could potentially provide an unambiguous association between CBCs and FRBs, if one exists, or unambiguously rule out FRB counterparts to a given CBC GW event. We demonstrate that, if a CBC that emitted both GWs and FRBs, is gravitationally lensed, we can make a $> 5\sigma$ association using time-delay estimates of the lensed GW and FRB images (in strong lensing), which are expected to be measured with mili-second (for GW) and nano-second (FRB) precisions. We also demonstrate that the CBC-FRB association can be made in the microlensing regime as well where wave-optics effects modulate the GW waveform. We further investigate the rate of such detected associations in future observing scenarios of both GW and radio detectors.