= Christoffel trace identity
{c}
{title2=$\Gamma^\rho{}_{\rho\mu}=\partial_\mu\log\sqrt{|g|}$}
For a nondegenerate <metric tensor> and its <Levi-Civita connection>, contracting the <Christoffel symbol> formula gives $\Gamma^\rho{}_{\rho\mu}=\tfrac12g^{ab}\partial_\mu g_{ab}$. The <Jacobi determinant derivative formula> identifies this with $\partial_\mu\log\sqrt{|\det g|}$. The volume density, rather than the determinant without an absolute value, works in every fixed metric signature.
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