About Asymptotic continuation of Einstein equation

TL;DR

This paper extends Einstein's gravitational equations by incorporating the energy density of the gravitational field itself, leading to a new solution for the metric of a point source with a deep potential well.

Contribution

It introduces a modified Einstein equation including gravitational energy density and derives a full metric solution for a point source.

Findings

Derived a full metric solution for a point source

Found a potential well with depth and size significantly different from Schwarzschild predictions

Extended Einstein's equations to include gravitational energy density

Abstract

The energy density of the gravitational field is a full-fledged source of the gravitational field. This principle of Einstein was not implemented by him in the Einstein equation. Not long ago it was possible to find an energy-momentum tensor that is asymptotically equal to part of the Ricci tensor. This tensor was included in Einstein's equation. As a result, Einstein's equation was shortened. The shortened gravitational field equation was initially solved only for the g_{00} field of a point source. Here we obtain the full metric of the gravitational field of a point source using a shortened field equation. The solution is interpreted as a potential well of extreme depth with a radius approximately forty times the Schwarzschild radius.