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

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

2007-09-10

arxiv.org/abs/0709.1403v2

Class.Quant.Grav.24:6255-6266,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, 2 figures. The presentation has been improved in all sections

Scientific paper

10.1088/0264-9381/24/24/008

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.

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