= Solution
The <equivalence principle> permits <Riemann normal coordinates> at any event, in which the first derivatives of the <metric tensor>, and hence the <Christoffel symbols>, vanish. A putative universal local gravitational <stress-energy tensor> constructed from the metric and its first derivatives would vanish in that freely falling description. If it were a genuine <tensor>, it would then vanish in every description, even where other coordinates assign nonzero gravitational energy density. The gravitational field therefore does not have a local <stress-energy tensor> analogous to that of matter, with coordinate-independent energy density and the usual energy-balance interpretation.
\b[Gravitational energy is not represented by a universal local covariant stress-energy tensor.] This does not assert that all local curvature tensors vanish or are forbidden: the <Riemann curvature tensor> measures tidal gravity, and higher-curvature tensors can be constructed. They do not provide the sought ordinary local gravitational energy density. Boundary charges, quantities associated with a background, and suitable averaged wave energies have different definitions and evade that local requirement. This is the <absence of a local gravitational stress-energy tensor>.
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