Renormalization Group Running of Newton's G: The Static Isotropic Case

TL;DR

This paper investigates how quantum gravity effects cause Newton's gravitational constant to vary with distance, linking the scale dependence to a gravitational vacuum condensate and comparing it with known effects in gauge theories.

Contribution

It introduces a non-perturbative analysis of the renormalization group running of Newton's G in the static isotropic case, connecting quantum gravity effects to vacuum condensates and effective field equations.

Findings

Newton's G increases slowly with distance due to quantum effects.

Vacuum solutions impose constraints on the scaling exponent ν.

Analogies are drawn between quantum gravity and non-abelian gauge theories.

Abstract

Corrections are computed to the classical static isotropic solution of general relativity, arising from non-perturbative quantum gravity effects. A slow rise of the effective gravitational coupling with distance is shown to involve a genuinely non-perturbative scale, closely connected with the gravitational vacuum condensate, and thereby, it is argued, related to the observed effective cosmological constant. Several analogies between the proposed vacuum condensate picture of quantum gravitation, and non-perturbative aspects of vacuum condensation in strongly coupled non-abelian gauge theories are developed. In contrast to phenomenological approaches, the underlying functional integral formulation of the theory severely constrains possible scenarios for the renormalization group evolution of couplings. The expected running of Newton's constant $G$ is compared to known vacuum polarization induced effects in QED and QCD. The general analysis is then extended to a set of covariant non-local effective field equations, intended to incorporate the full scale dependence of $G$, and examined in the case of the static isotropic metric. The existence of vacuum solutions to the effective field equations in general severely restricts the possible values of the scaling exponent $\nu$.