= Covariant divergence formula
{title2=$\nabla_\mu A^\mu=|g|^{-1/2}\partial_\mu(\sqrt{|g|}A^\mu)$}
The <Christoffel trace identity> converts the <covariant derivative> of a <vector field> into a coordinate divergence weighted by the metric volume density. This is valid for the <Levi-Civita connection>. Applied to the raised gradient of a <scalar field>, it gives $\Box\phi=|g|^{-1/2}\partial_\mu(\sqrt{|g|}g^{\mu\nu}\partial_\nu\phi)$ in Lorentzian signature, the curved <d'Alembert operator>.
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