Electron-positron pairs production in a macroscopic charged core

TL;DR

This paper investigates electron-positron pair production around a macroscopic charged core, showing that quantum tunneling can lead to significant pair creation rates surpassing Hawking radiation under certain conditions.

Contribution

It introduces a semi-classical analysis of bound states in a charged core and explicitly calculates pair-production rates, comparing them with known quantum electrodynamics and Hawking processes.

Findings

Semi-classical bound states can have energies below -mc^2.

Pair-production rate exceeds Hawking radiation for certain charge-to-mass ratios.

Quantum tunneling significantly contributes to electron-positron pair creation.

Abstract

Classical and semi-classical energy states of relativistic electrons bounded by a massive and charged core with the charge-mass-radio Q/M and macroscopic radius R_c are discussed. We show that the energies of semi-classical (bound) states can be much smaller than the negative electron mass-energy (-mc^2), and energy-level crossing to negative energy continuum occurs. Electron-positron pair production takes place by quantum tunneling, if these bound states are not occupied. Electrons fill into these bound states and positrons go to infinity. We explicitly calculate the rate of pair-production, and compare it with the rates of electron-positron production by the Sauter-Euler-Heisenberg-Schwinger in a constant electric field. In addition, the pair-production rate for the electro-gravitational balance ratio Q/M = 10^{-19} is much larger than the pair-production rate due to the Hawking processes.