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. These identities are named after Luigi Bianchi, although they had been already derived by Aurel Voss in 1880, and independently by Gregorio Ricci-Curbastro in 1889.

Source: Wikipedia — Contracted Bianchi identities (CC BY-SA 4.0)