Gravitational self-lensing of Fast Radio Bursts in neutron star magnetospheres: I. The model

Fast Radio Bursts (FRBs) are cosmological sub-second bursts of coherent radio emission, whose source is still unknown. To date, the galactic magnetar SGR 1935+2154 is the only astrophysical object known to emit radio bursts akin to FRBs, albeit less powerful, supporting suggestions that FRBs originate from magnetars. Many remarkable properties of FRBs, e.g. the dichotomy between repeaters and one-off sources, and their power-law energy distributions (with typical index $\sim 2-3$), are not well understood yet. Moreover, the huge radio power released by the most active repeaters is challenging even for the magnetic energy reservoir of magnetars. Here we assume that FRBs originate from co-rotating hot-spots anchored in neutron star magnetospheres and get occasionally amplified by large factors via gravitational self-lensing in the strong NS field. We evaluate the probability of amplification and show that (i) a power-law energy distribution of events $\propto E^{-(2- 3)}$ is generally expected, (ii) all FRB sources may be regarded as repeating, their appearance as one-off sources or repeaters being determined by the critical dependence of the amplification probability on the emission geometry and source orientation relative to Earth and (iii) the most active repeaters, in particular, correspond to extremely rare and finely-tuned orientations ($\sim$ one in $10^6$), leading to large probabilities of amplification which make their bursts frequently detectable. At the same time, their power release appears enhanced, typically by factors $\gtrsim 10$, easing their energy budget problem.