High Sensitivity Methodologies to Detect Radio Band Gravitational Waves

Gravitational waves (GWs) can resonate with magnetic fields through the Gertsenshtein-Zeldovich effect, producing electromagnetic signals at the same frequency. In pulsar magnetospheres, this conversion may yield a faint radio-band signal that could be detected. In this work, we focus on two specific pulsars, PSR J1856-3754 and PSR J0720-3125, and use numerical simulations to evaluate how well the FAST and SKA2-MID telescopes could detect such signals. We consider transient events, including primordial-black-hole-like mergers, as well as stochastic backgrounds, including primordial GWs. To improve detection sensitivity, we propose four observational methods to lower the detectable energy-density limit of very high-frequency (VHF) GWs; the "Multiple Pulsars with Multiple Telescopes" (MPMT) method performs best because it allows cross-validation and rejection of false candidates. Under the assumption of nearly 6000 hours of observation at 3 GHz and a $5\sigma$ detection threshold, the minimum detectable characteristic strain is projected to be $h_c \approx 10^{-23}$ for transient events and $h_c \approx 10^{-33}$ for stochastic backgrounds. Under optimistic assumptions on integration time and conversion efficiency, these projections suggest that radio-band searches may approach the sensitivity needed to begin testing representative VHF GW scenarios. More broadly, this conversion in pulsar magnetospheres could be relevant to the origin of some repeating fast radio bursts in the our galaxy.