The modification of Einstein`s gravitational field equation following from the energy conservation law

TL;DR

This paper proposes a modified gravitational field equation that aligns with energy conservation laws, providing solutions for cosmic objects that differ from Einstein's equations but remain physically meaningful.

Contribution

It introduces a new gravitational field equation consistent with energy conservation, extending Einstein's framework for cosmic objects.

Findings

Modified equations differ from Einstein's for black holes and strings

Results have physical meaning and are consistent with conservation laws

Differences are significant for certain cosmic objects

Abstract

The cause of an infringement in GR of a gravitational field energy conservation law is investigated . The equation of a gravitational field not contradicting to the energy conservation law is suggested. This equation satisfy to the Einstein,s requirement of equivalence of all energy kinds as sources of a gravitational field. This equation is solved in paper for cosmic objects. It is showed, that results for some objects - for black holes and gravitating strings-essentialy differ from such for Einstein,s equation, have the symple meaning and do not contradictions.