Classical Electron Model with QED Corrections

Abstract

In this article we build a metric for a classical general relativistic electron model with QED corrections. We calculate the stress-energy tensor for the radiative corrections to the Coulomb potential in both the near-field and far-field approximations. We solve the three field equations in both cases by using a perturbative expansion to first order in alpha (the fine-structure constant) while insisting that the usual (+, +, -, -) structure of the stress-energy tensor is maintained. The resulting metric models a (non-spinning) electron with a Coulomb potential with QED corrections, and maintains masslessness of the photon to self-consistent order. The near-field solution resembles the metric of a global monopole.