Spherically symmetric ADM gravity with variable G and Λc

This paper investigates the Arnowitt-Deser-Misner (hereafter ADM) form of spherically symmetric gravity with variable Newton parameter G and cosmological term Λc. 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, which 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