Newtonian-like gravity with variable G

Abstract

We propose a Lagrangian formulation for a varying G Newtonian-like theory inspired by the Brans-Dicke gravity. Rather than imposing an ad hoc dependence for the gravitational coupling, as previously done in the literature, in our proposal the running of G emerges naturally from the internal dynamical structure of the theory. We explore the features of the resulting gravitational field for static and spherically symmetric mass distributions as well as within the cosmological framework.

Stellar Structure in a Newtonian Theory with Variable G

“…As already pointed out in Ref. [10], in a vacuum, Equations ( 5) and ( 6) are decoupled. Thus, the fields ψ and σ have independent dynamics, both satisfying Laplace's equations.…”

“…In Ref. [10], a Lagrangian for a theory with varying G has been proposed and is reviewed in this Section. The Lagrangian of this new approach is given by…”

“…Let us start by reviewing the simple realization of a static sphere of radius R with constant density ρ 0 . As shown in [10], the gravitational potential in this case assumes the form…”

“…In a recent paper [10], a new Newtonian theory with varying gravitational coupling has been proposed. The gravitational coupling, now given by a function of time and position, is dynamically determined together with the gravitational potential from a new gravitational Lagrangian.…”

“…In this paper, we focus on the stellar structure of non-relativistic stars. This is an important analysis in the context of the theory proposed in [10] since it has been shown that the main difference from the standard Newtonian gravity should manifest within matter distributions.…”