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Contracted Bianchi identities

In general relativity and tensor calculus, the contracted Bianchi identities are: ∇ ρ R ρ μ = 1 2 ∇ μ R {\displaystyle \nabla _{\rho }{R^{\rho }}_{\mu }={1 \over 2}\nabla _{\mu }R} where R ρ μ {\displaystyle {R^{\rho }}_{\mu }} is the Ricci tensor, R {\displaystyle R} the scalar curvature, and ∇ ρ {\displaystyle \nabla _{\rho }} indicates covariant differentiation.

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