The trivial solution of the gravitational energy-momentum tensor problem

TL;DR

This paper shows that by relaxing certain assumptions, the gravitational energy-momentum tensor can be trivially defined as the Einstein tensor, offering a new perspective on energy conservation in gravity.

Contribution

It demonstrates that the gravitational energy-momentum tensor can be trivially identified with the Einstein tensor when relaxing derivative dependence assumptions.

Findings

The gravitational energy-momentum tensor is essentially the Einstein tensor.

Peculiarities of this definition have sensible physical interpretations.

Challenges the common view that no such tensor exists for gravity.

Abstract

In the literature one often finds the claim that there is no such thing as an energy-momentum tensor for the gravitational field, and consequently, that the total energy-momentum conservation can only be defined in terms of a gravitational energy-momentum pseudo-tensor. Nevertheless, by relaxing the assumption that gravitational energy-momentum tensor should only depend on first derivatives of the metric, the Einstein equation leads to a trivial result that gravitational energy-momentum tensor is essentially the Einstein tensor. We discuss various peculiarities of such a definition of energy-momentum are argue that all these peculiarities have a sensible physical interpretation.