Foundations of the theory of gravity with a constraint. Gravitational energy of macroscopic bodies

The paper considers a set of equations describing the static isotropic gravity field of a macroscopic body within the framework of the theory of gravity with a constraint. A general approximate solution of these equations is obtained. The solution exists only at certain values for the three integration constants. The out-of-body metric coincides with the Schwarzschild metric, but, unlike the general relativity theory (GR), the curvature tensor invariants have a certain finite value everywhere.