On the dissimilarity between the algorithms for computing the symmetric energy-momentum tensor in ordinary field theory and general relativity

The recipe used to compute the symmetric energy-momentum tensor in the framework of ordinary field theory bears little resemblance to that used in the context of general relativity, if any. We show that if one starts from the field equations instead of the Lagrangian density, one obtains a unified algorithm for computing the symmetric energy-momentum tensor in the sense that it can be used for both usual field theory and general relativity.