Spherically symmetric ADM gravity with variable G and Lambda(c)

TL;DR

This paper explores a spherically symmetric ADM gravity model with a variable Newton's G and cosmological constant, deriving solutions and discussing potential observational implications of a dynamical G.

Contribution

It introduces a Hamiltonian formulation with a dynamical G, finding exact solutions and analyzing their physical and observational consequences.

Findings

Existence of a static solution reducing to Schwarzschild geometry

Derivation of an exact G(r) solution for zero cosmological constant

Identification of a nearly linear growth law for G at large r

Abstract

This paper investigates the Arnowitt--Deser--Misner (hereafter ADM) form of spherically symmetric gravity with variable Newton parameter G and cosmological term Lambda(c). The Newton parameter is here treated as a dynamical variable, rather than being merely an external parameter as in previous work on closely related topics. The resulting Hamilton equations are obtained; interestingly, a static solution exists, that reduces to Schwarzschild geometry in the limit of constant G, describing a Newton parameter ruled by a nonlinear differential equation in the radial variable r. A remarkable limiting case is the one for which the Newton parameter obeys an almost linear growth law at large r. An exact solution for G as a function of r is also obtained in the case of vanishing cosmological constant. Some observational implications of these solutions are obtained and briefly discussed.