A new approach to the theory with variable gravitational constant

A theory with variable gravitational constant is presented, which is based on the bimetric formulation of general relativity, and which is in agreement with Newtonian and post-Newtonian approximations of the theory of gravitation for the parameter absolute value of zeta much greater than 4 x 10 to the -6th. It is shown that the total action S = -M (tau), where tau is the time in the remote system of reference, relative to which the celestial body is in rest. This equation is in agreement with the Brans- Dicke theory. The Tolman formula, in the framework of GR, is also true for the bimetric theory with the variable gravitational constant. External analytical and internal numerical solutions of the field equations are found for the case of incompressible matter. It is also shown that generalized bimetric theory of gravitation does not exclude the possibility of existence of static, supermassive, and superdense configurations. (N.B.)