Corrections to Hawking radiation from asteroid-mass primordial black holes: Formalism of the exchange interaction

The search for dark matter remains at the forefront of cosmological research. Primordial black holes (PBHs) in the asteroid mass range are candidates that could account for all—or a large fraction of—dark matter, while still falling within modern observational constraints. PBHs with masses on the order of 10¹⁷ g have a Hawking temperature such that they emit non-negligible Hawking radiation in the form of photons, electrons, positrons and neutrinos. We are using perturbative quantum electrodynamics to model the expected photon, electron and positron spectra emitted by uncharged, non-rotating PBHs to first order in the fine structure constant. We present the analytic expression for the specific corrections to the electron/positron spectra due to Coulomb- and exchange interactions. This project aims to produce numerically generated first order corrections to the electron/positron spectra. These results will have significant application in the modeling of the 511keV positron annihilation line, which can be used for observational comparison to determine whether PBHs form a significant fraction of dark matter.