Probing quantum gravity at low energies

Abstract: Planck stars form when a collapsing shell of matter within a black hole reaches the Planck density, roughly equivalent to the mass being compressed into a volumetric size near that of the proton, and rebounds outwards. These planck stars have been considered as accounting for both fast radio bursts and short gamma ray bursts, whilst offering a comparatively low energy perspective onto quantum gravity. The observation of such an event would require black hole masses much smaller than a solar mass, which could be provided by primordial black hole dark matter models. We discuss the low energy isotropic background emissions produced by decaying primordial black holes at all epochs and derive constraints from the spectrum of the extragalactic background light. We find that, in order to avoid exceeding known extragalactic background light emissions, we must restrict the total energy emitted at low frequencies by a planck star exploding in the present epoch to be less than $10^{13}$ erg or restrict the primordial black hole population far below any existing limits. This casts doubt on whether exploding planck stars could actually account for fast radio bursts, as they are speculated to in the literature.