Quantum Corrections to the Schwarzschild and Kerr Metrics

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_{μν} 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.

Figures (4)

• Figure 1: The vacuum polarization diagram.
• Figure 2: Vacuum polarization modification of the energy-momentum tensor.
• Figure 3: Diagrams contributing to the one-particle-reducible potential.
• Figure 4: Gravitational radiative correction diagrams leading to nonanalytic components of form factors.