Quantum corrections to the Reissner–Nordström and Kerr–Newman metrics

We use effective field theory techniques to examine the quantum corrections to the gravitational metrics of charged particles, with and without spin. In momentum space the masslessness of the photon implies the presence of non-analytic pieces ∼−q2, q2log(−q2), etc. in the form factors of the energy–momentum tensor. We show how the former reproduces the classical non-linear terms of the Reissner–Nordström and Kerr–Newman metrics while the latter can be interpreted as quantum corrections to these metrics, of order Gαℏ/mr3.