Quantum Corrections to the Schwarzschild and Kerr Metrics

TL;DR

This paper investigates quantum corrections to classical black hole metrics, revealing new quantum effects and proposing a way to define a running gravitational charge based on gravitational radiative corrections.

Contribution

It demonstrates how quantum radiative corrections modify classical Schwarzschild and Kerr metrics, introducing long-range quantum effects and defining a running gravitational charge.

Findings

Classical corrections match known solutions from general relativity.

Quantum effects introduce new long-range modifications to the metric.

A framework for a running gravitational charge is proposed.

Abstract

We examine the corrections to the lowest order gravitational interactions of massive particles arising from gravitational radiative corrections. We show how the masslessness of the graviton and the gravitational self interactions imply the presence of nonanalytic pieces sqrt{-q^2}, ln-q^2, etc. in the form factors of the energy-momentum tensor and that these correspond to long range modifications of the metric tensor g_{\mu\nu} of the form G^2m^2/r^2, G^2m\hbar/r^3, etc. The former coincide with well known solutions from classical general relativity, while the latter represent new quantum mechanical effects, whose strength and form is necessitated by the low energy quantum nature of the general relativity. We use these results to define a running gravitational charge.