Semi-Classical Solution to a Schwarzschild Problem Almost Entirely Congruent to the New Law of Gravity

One of spherically symmetric solutions of field equation corresponds to Schwarzschild solution, while most part of its Christoffel symbols are asymptotically equal to Christoffel symbols of Schwarzschild’s metric tensor. In particular, the gravity field acceleration given by the new solution coincides with the gravity field acceleration given by the Schwarzschild solution in weak fields. For homogeneous space, the field equation returns the metric with exponential dependence on time, which is imposed by space. Einstein’s equation in the new version performs another function: it allows calculating the full tensor of energy-momentum of matter and field via a metric tensor. Namely the new solution with the spherical symmetry in space without matter is the field of “gravity” forces oriented outwards. In this case, a role of “dark energy” is played by the gravity field negative energy density. Sizes of this object are proportional to absolute value of field energy and not limited at all. It is assumed that namely such solutions are responsible for the large-scale structure of the Universe. Gravity field energy density was computed in the frame of the Newtonian gravity theory. The Newtonian gravity law was deduced with a correction for a non-zero density of a gravity field. The new gravity law is virtually almost entirely congruent with the Schwarzschild mutual attraction law in a zone somewhat distant from the Schwarzschild radius. The assumption was outspoken that the Einstein’s refusal from the energy of a gravitational field as a field source in the Einstein’s equation could result in noticeable errors in solutions of this equation.