# Conservation law of energy-momentum in general relativity

## TL;DR

This paper discusses the importance of semi-metric in general relativity and derives a general covariant energy-momentum conservation law that addresses previous limitations.

## Contribution

It introduces a semi-metric approach to derive a universally valid covariant energy-momentum conservation law in general relativity.

## Key findings

- Derivation of a general covariant conservation law of energy-momentum.
- Addresses flaws in Einstein, Landau, and Moller formulations.
- Highlights the necessity of semi-metric in the theory.

## Abstract

We explain the necessity of application of semi-metric in general relativity. A detailed discussion on the energy-momentum conservation in the general relativity is presented using the mathematical tool of semi-metric. By means of the general covariant spacetime translation transformation, the most general covariant conservation law of energy-momentum is obtained, which is valid for any coordinates and overcomes the flaws of the expressions of Einstain, Landau and Moller.