Quantum Corrections to the Reissner-Nordstr\"{o}m and Kerr-Newman Metrics

TL;DR

This paper investigates quantum corrections to the classical Reissner-Nordström and Kerr-Newman metrics for charged particles using effective field theory, identifying nonanalytic form factors that encode classical and quantum modifications.

Contribution

It demonstrates how quantum effects modify classical charged black hole metrics through nonanalytic form factors in the energy-momentum tensor.

Findings

Classical non-linear terms are reproduced by nonanalytic pieces in form factors.

Quantum corrections are of order Gαħ/mr^3.

Quantum effects can be interpreted as modifications to classical metrics.

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-Nordstr\"{o}m and Kerr-Newman metrics while the latter can be interpreted as quantum corrections to these metrics, of order $G\alpha\hbar/mr^3$