Corrections to Hawking Radiation from Asteroid Mass Primordial Black Holes: I. Formalism of Dissipative Interactions in Quantum Electrodynamics

TL;DR

This paper develops a formalism to incorporate dissipative interactions in quantum electrodynamics, specifically addressing corrections to Hawking radiation from primordial black holes in the mass range relevant for dark matter, enhancing the accuracy of emission spectra modeling.

Contribution

It introduces a rigorous quantum electrodynamics framework to compute dissipative corrections to Hawking radiation from primordial black holes, including the effects of electron-positron pair creation and annihilation.

Findings

Derived an analytic expression for dissipative corrections to Hawking radiation.

Quantified the impact of electron-positron plasma interactions on emission spectra.

Provided a foundation for more accurate modeling of black hole evaporation signals.

Abstract

Primordial black holes (PBHs) within the mass range $10^{17} - 10^{22}$ g are a favorable candidate for describing the all of the dark matter content. Towards the lower end of this mass range, the Hawking temperature, $T_{\rm H}$, of these PBHs is $T_{\rm H} \gtrsim 100$ keV, allowing for the creation of electron -- positron pairs; thus making their Hawking radiation a useful constraint for most current and future MeV surveys. This motivates the need for realistic and rigorous accounts of the distribution and dynamics of emitted particles from Hawking radiation in order to properly model detected signals from high energy observations. This is the first in a series of papers to account for the $\mathcal{O}(\alpha)$ correction to the Hawking radiation spectrum. We begin by the usual canonical quantization of the photon and spinor (electron/positron) fields on the Schwarzschild geometry. Then we compute the correction to the rate of emission by standard time dependent perturbation theory from the interaction Hamiltonian. We conclude with the analytic expression for the dissipative correction, i.e. corrections due to the creation and annihilation of electron/positrons in the plasma.