The trivial solution of the gravitational energy-momentum tensor problem

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.