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In [[general relativity]] and [[tensor calculus]], the '''[[Attilio Palatini|Palatini]] identity''' is:

: <math>\delta R_{\mu\nu}{} = (\delta\Gamma^{\lambda}{}_{\mu\nu})_{;\lambda} - (\delta\Gamma^{\lambda}{}_{\mu\lambda})_{;\nu}</math>

where <math>\delta\Gamma^{\lambda}{}_{\mu\nu}</math> denotes the variation of [[Christoffel symbols]]<ref name="christoffel" >{{citation|title=Ueber die Transformation der homogenen Differentialausdrücke zweiten Grades|last=Christoffel|first=E.B.|author-link=Elwin Bruno Christoffel|journal=Jour. für die reine und angewandte Mathematik|volume=B. 70|pages=46–70|year=1869|url=http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=GDZPPN002153882&IDDOC=266356}}</ref> and semicolon ";" indicates [[covariant differentiation]].

==See also==
*[[Palatini variation]]
*[[Ricci calculus]]
*[[Tensor calculus]]

==Notes==
{{Reflist}}

==References==
* A. Palatini (1919) ''Deduzione invariantiva delle equazioni gravitazionali dal principio di Hamilton'', Rend. Circ. Mat. Palermo '''43''', 203-212 [English translation by R.Hojman and C. Mukku in [[Peter Bergmann|P.G. Bergmann]] and V. De Sabbata (eds.) Cosmology and Gravitation, Plenum Press, New York (1980)]
* M. Tsamparlis, ''On the Palatini method of Variation'', J. Math. Phys. '''19''', 555 (1977).

[[Category:Concepts in physics]]
[[Category:Tensors| ]]
[[Category:General relativity| ]]