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In general relativity and tensor calculus, the Palatini identity is:
where δ Γ ν σ ρ {\displaystyle \delta \Gamma _{\nu \sigma }^{\rho }} denotes the variation of Christoffel symbols and ∇ ρ {\displaystyle \nabla _{\rho }} indicates covariant differentiation.
A proof can be found in the entry Einstein–Hilbert action.
The "same" identity holds for the Lie derivative L ξ R σ ν {\displaystyle {\mathcal {L}}_{\xi }R_{\sigma \nu }}. In fact, one has:
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