= Absence of a local gravitational stress-energy tensor
The <Equivalence principle> allows <Riemann normal coordinates> in which the first derivatives of the <metric tensor> vanish at a chosen point. A purported local gravitational <stress-energy tensor> built from those first derivatives would vanish there in that chart and therefore, if tensorial, in all charts. Such an expression cannot encode the gravitational energy assigned by a coordinate-dependent field description. This rules out an ordinary universal local covariant gravitational energy density, not the construction of local curvature tensors or boundary and averaged notions of gravitational energy. The <Riemann curvature tensor> still describes invariant tidal gravity.
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