Abstract
Quantum corrections to the classical field equations, induced by a scale dependent gravitational constant, are analyzed in the case of the static isotropic metric. The requirement of general covariance for the resulting non-local effective field equations puts severe restrictions on the nature of the solutions that can be obtained. In general the existence of vacuum solutions to the effective field equations restricts the value of the gravitational scaling exponent ν −1 to be a positive integer greater than one. We give further arguments suggesting that in fact only for ν −1 = 3 consistent
Highlights
Quantum corrections to the classical field equations, induced by a scale dependent gravitational constant, are analyzed in the case of the static isotropic metric
The main aspect we wish to investigate in this paper is the nature of the specific predictions about the running of Newton’s constant G, as they apply to the standard static isotropic metric
Our starting point will be the solution of the non-relativistic Poisson equation, which for a localized point source can be investigated for various values of the gravitational scaling exponent ν
Summary
Quantum corrections to the classical field equations, induced by a scale dependent gravitational constant, are analyzed in the case of the static isotropic metric. To check the overall consistency of the results, a different approach to the solution of the covariant effective field equations for the static isotropic metric will be pursued, in terms of an effective vacuum density and pressure.
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