Quantum Corrections to the Reissner-Nordström and Kerr-Newman Metrics

TL;DR

The paper addresses quantum corrections to the spacetime metric around charged particles using an effective field theory framework. It computes energy-momentum tensor form factors in QED, identifies nonanalytic structures arising from massless photons, and maps these to metric corrections via the linearized Einstein equations and Fourier transforms. The leading nonanalytic square-root term reproduces the classical Reissner-Nordström and Kerr-Newman metrics, while a logarithmic term yields quantum corrections of order $G\alpha\hbar/(mr^3)$; for spin-1/2, Kerr-Newman is recovered with additional spin-dependent contributions. This work demonstrates a calculable separation of classical and quantum long-range gravitational effects within EFT, laying groundwork for higher-order graviton-loop analyses.

Abstract

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 nonanalytic pieces $\sim \sqrt{-q^2},q^2\log -q^2$ 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 $Gα\hbar/mr^3$

Figures (2)

• Figure 1: Feynman diagrams for spin 0 radiative corrections to $T_{\mu\nu}$.
• Figure 2: Feynman diagrams for spin 1/2 radiative corrections to $T_{\mu\nu}$.