Schwinger's consistency requirement and gravitation

According to Schwinger, equal time commutator of the symmetric Rosenfeld energy-momentum tensor of matter of lower spins has a particularly simple form due to the Lorentz invariance. He claimed that this relation is not applicable for gravity. We derive here a classical Poisson bracket relation, analog of the Schwinger condition, which holds for non symmetrical canonical energy-momentum tensor of the general Poincare' invariant theory of gravitation assuming minimal numbers of constraints in the theory. (authors)