The energy-momentum tensor of the gravitational field as a correction to the Einstein equation

Abstract

The energy-momentum-stress tensor of the Riemannian space is found and defined in the general theory of relativity as a function of the metric tensor. In inertial space, this tensor is equal to zero, but in the Newtonian limit, its energy density value is calculated. The general theory of relativity makes it possible to include the field energy tensor in the gravitational field equation. The new gravitational field equation is asymptotically equal to the Einstein equation when applied in weak fields. The region 0<r<rg is occupied by a potential well, which has an extremely low potential, this fact suggests that neutron stars and heavier objects have the same structure. The introduction of the new equation of the gravitational field and the energy-momentum tensor of the gravitational field into the classical Einsteinian relativistic theory of gravitation led us to a consistent continuation of the general theory of relativity.