Abstract
The invariant projections of the generalized canonical, symmetric, and variational energy-momentum tensor and their divergences are investigated in spaces with affine connection and metric. Connections between the obtained quantities are found on the basis of the generalized covariant Bianchi-type identities and the covariant Euler–Lagrange equations. It can be shown that the weak principle of equivalence can be considered as a corollary of the Euler–Lagrange equations for a given field theory.
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