EP and active/passive mass

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If we start from an action in which geometry and matter are non-minimally coupled, can the resulting theory have a covariantly conserved stress-energy tensor (if so, what is the stress-energy tensor in terms of the action?)

In Newtonian physics the EP (equivalence of inertial/passive mass) and the third law (equivalence of passive/active mass, momentum conservation) are not linked. I'd naively guess that violating the EP (minimal coupling) will cause non-conservation of stress-energy-momentum so that these are linked in GR, if not in Newtonian gravity.

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