Invariant projection of the energy‐momentum tensors for field theories in spaces with affine connection and metric

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.