The physical significance of the Babak-Grishchuk gravitational energy-momentum tensor

TL;DR

This paper critically analyzes the Babak-Grishchuk gravitational energy-momentum tensor, demonstrating that it lacks physical significance due to its gauge dependence, and clarifies its relation to General Relativity.

Contribution

The paper shows that the Babak-Grishchuk tensor is gauge-dependent and equivalent to GR, challenging claims of its physical significance in localizing gravitational energy.

Findings

The tensor is gauge-dependent and not physically meaningful.

It is equivalent to General Relativity at the action level.

Gauge transformations alter the tensor's form without physical implications.

Abstract

We examine the claim of Babak and Grishchuk [1] to have solved the problem of localising the energy and momentum of the gravitational field. After summarising Grishchuk's flat-space formulation of gravity, we demonstrate its equivalence to General Relativity at the level of the action. Two important transformations are described (diffeomorphisms applied to all fields, and diffeomorphisms applied to the flat-space metric alone) and we argue that both should be considered gauge transformations: they alter the mathematical representation of a physical system, but not the system itself. By examining the transformation properties of the Babak-Grishchuk gravitational energy-momentum tensor under these gauge transformations (infinitesimal and finite) we conclude that this object has no physical significance.