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According to a recent suggestion [1], the energy--momentum tensor forgravitating fields can be computed through a suitable rearrangement of thematter field equations, without relying on the variational definition. We showthat the property observed by Accioly et al. in [1] is the consequence of ageneral identity, which follows from the covariance of the matter Lagrangian inmuch the same way as (generalized) Bianchi identities follow from thecovariance of the purely gravitational Lagrangian. However, we also show thatonly in particular cases can this identity be used to obtain the actual form ofthe stress-energy tensor, while in general the method leads to ambiguities andpossibly to wrong results. Moreover, in nontrivial cases the computations turnout to be more difficult than the standard variational technique.Comment: 5 pages, plain Tex, no figures, to appear in GRG Journa

Can the Local Energy-Momentum Conservation Laws be Derived Solely from Field Equations?