Abstract Gravitational lensing of short astrophysical transients provides a uniquely direct avenue for searching for primordial black holes (PBHs) across a vast range of masses. While past search efforts have focused on particular source classes — such as fast radio bursts (FRBs) and gamma-ray burst spikes — no systematic, multi-wavelength assessment has compared their relative potential for PBH discovery. We present here a broad assessment of transient lensing search opportunities, spanning more than twenty decades in photon frequency and over twelve orders of magnitude in PBH mass. For each class, we determine the accessible PBH mass window by accounting for wave-optics suppression and time-delay resolution limits, and we estimate potential sensitivities to the PBH abundance using representative event rates, distances, and optical depths. Our survey includes low-frequency radio events (FRBs, pulsar giant pulses, planetary cyclotron bursts), optical/infrared signals, and high-energy phenomena (gamma-ray burst spikes, fast X-ray transients, TeV blazar flares). We synthesize these results in a unified mass-abundance diagram and comprehensive tables summarizing both physical reach and observational requirements. This work serves as a roadmap for optimizing future multi-wavelength lensing searches, guiding the design of instruments and strategies to explore the PBH dark matter hypothesis across its remaining viable parameter space.
Stefano Profumo (2025) studied this question.