Exact equation of the gravitational field
Exact equation of the gravitational field based on the Einstein separation of the Ricci tensor
Morozov V. B.
In 1915 Einstein divided the left-hand side of the gravitational field equation (the Ricci
tensor) into two tensors, one of which goes to zero with a certain choice of coordinates. The
property of this part of the Ricci tensor suggests that this part is related to the gravitational field,
since it is known that only the energy-momentum tensor of the gravitational field can be zeroed
by transforming coordinates. This allows the energy-momentum tensor of the gravitational field
to be brought into the Einstein equation. The new equation is asymptotically equivalent to the
Einstein equation at low energy of the gravitational field. In addition, the local energy-momentum
conservation law results directly from this equation. The covariance of the equation is proven. A
numerical solution of the equation is provided for . This solution could change our
understanding of the behavior of the gravitational field near the source. In contrast to the
Schwarzschild solution , it does not reverse the sign here, becoming meaningless, but rapidly
decreases to a value of almost zero, remaining non-negative. This feature lies at a distance from
the origin of coordinates that is noticeably greater than the Schwarzschild radius.
Key terms: general theory of relativity, gravitational field equation, Einstein equation, Ricci
tensor, rigorous solutions.