Physical significance of the Babak-Grishchuk gravitational energy-momentum tensor

We examine the claim of Babak and Grishchuk [S. V. Babak and L. P. Grishchuk, Phys. Rev. D 61, 024038 (1999)] to have solved the problem of localizing the energy and momentum of the gravitational field. After summarizing 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.