  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.
