= Stress-energy tensor of a nonminimally coupled scalar field
{title2=$T_{ab}=\nabla_a\Phi\nabla_b\Phi-\frac12g_{ab}(\nabla\Phi)^2+2\xi[\Phi^2G_{ab}+g_{ab}\Box(\Phi^2)-\nabla_a\nabla_b(\Phi^2)]$}
For action $S=\int\sqrt{-g}[-\frac12(\nabla\Phi)^2-\xi R\Phi^2]d^4x$, <metric variation> defines $\delta S=\frac12\int\sqrt{-g}T^{ab}\delta g_{ab}d^4x$ and gives the displayed tensor. The <contracted Bianchi identity> and the scalar derivative commutator yield $\nabla^aT_{ab}=(\Box\Phi-2\xi R\Phi)\nabla_b\Phi$, so the <stress-energy tensor> is conserved on the field equation.
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