A new approach to the theory with variable gravitational constant

A theory with variable gravitational constant, based on the bimetric formulation of general relativity, is suggested. It is in agreement with the Newtonian and post-Newtonian approximations of the theory of gravitation when the theory parameter ||4×10^–6. The statical spherical-symmetric distribution of gravitating masses is investigated. It is shown that the total action (including the own gravitational field of the system)S=–M, where is the time in the remote system of reference, relative to which the celestial body is in rest. In the Brans-Dicke theory ||1 andS–M. The Tolman formula for the massM in the Einstein theory is also valid in the suggestedGeneralized Bimetric Theory of Gravitation. External analytical and internal numerical solutions of the field equations are found for the case of incompressible matter. It is shown that static and supermassive configurations may exist if –0.13<0.