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, 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.
Spherically symmetric ADM gravity with variable G and Lambda(c) / Esposito, G.; Rubano, Claudio; Scudellaro, Paolo. - In: CLASSICAL AND QUANTUM GRAVITY. - ISSN 0264-9381. - STAMPA. - 24:(2007), pp. 6255-6266. [10.1088/0264-9381/24/24/008]
Spherically symmetric ADM gravity with variable G and Lambda(c)
G. Esposito;RUBANO, CLAUDIO;SCUDELLARO, PAOLO
2007
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, 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.File | Dimensione | Formato | |
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