Renormalization group running of Newton’s constantG: The static isotropic case

Corrections are computed to the classical static isotropic solution ofgeneral relativity, arising from non-perturbative quantum gravity effects. Aslow rise of the effective gravitational coupling with distance is shown toinvolve a genuinely non-perturbative scale, closely connected with thegravitational vacuum condensate, and thereby, it is argued, related to theobserved effective cosmological constant. Several analogies between theproposed vacuum condensate picture of quantum gravitation, and non-perturbativeaspects of vacuum condensation in strongly coupled non-abelian gauge theoriesare developed. In contrast to phenomenological approaches, the underlyingfunctional integral formulation of the theory severely constrains possiblescenarios for the renormalization group evolution of couplings. The expectedrunning of Newton's constant $G$ is compared to known vacuum polarizationinduced effects in QED and QCD. The general analysis is then extended to a setof covariant non-local effective field equations, intended to incorporate thefull scale dependence of $G$, and examined in the case of the static isotropicmetric. The existence of vacuum solutions to the effective field equations ingeneral severely restricts the possible values of the scaling exponent $\nu$.Comment: 61 pages, 3 figure