= Diffeomorphism Noether identity for a scalar field
{title2=$\nabla^aT_{ab}=\frac1{\sqrt{-g}}\frac{\delta S}{\delta\Phi}\nabla_b\Phi$}
Simultaneously varying a <metric tensor> and a <scalar field> by the <Lie derivative> along a compactly supported <vector field> leaves a covariant matter action invariant. <Integration by parts> gives the displayed <Noether identity>. It implies <stress-energy conservation> when the scalar equation holds without needing to impose the metric field equation.
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