Proposal for the proper gravitational energy-momentum tensor

TL;DR

This paper introduces a new gravitational energy-momentum tensor in general relativity derived via Noether's theorem, which transforms as a tensor and satisfies conservation laws, with applications to gravitational waves and cosmology.

Contribution

It presents a novel tensor formulation for gravitational energy-momentum that adheres to tensor transformation rules and conservation laws, addressing previous ambiguities.

Findings

Tensor transforms as a tensor under coordinate changes

Conservation law is satisfied in local Lorentz frames

Energy calculations for gravitational wave and cosmological models

Abstract

We propose a gravitational energy-momentum tensor of the general relativity obtained using Noethers theorem. It transforms as a tensor under general coordinate transformations. One of the two indices of the gravitational energy-momentum tensor labels a local Lorentz frame that satisfies the energy-momentum conservation law. The energies for a gravitational wave and a Friedmann-Lemaitre--Robertson--Walker universe are calculated as examples.