Palatini identity

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In general relativity and tensor calculus, the Palatini identity is:

\delta R_{\mu\nu}{} = (\delta\Gamma^{\lambda}{}_{\mu\nu})_{;\lambda} - (\delta\Gamma^{\lambda}{}_{\mu\lambda})_{;\nu}

where \delta\Gamma^{\lambda}{}_{\mu\nu} denotes the variation of Christoffel symbols[1] and semicolon ";" indicates covariant differentiation.

See also[edit]

Notes[edit]

  1. ^ Christoffel, E.B. (1869), "Ueber die Transformation der homogenen Differentialausdrücke zweiten Grades", Jour. für die reine und angewandte Mathematik, B. 70: 46–70 

References[edit]

  • 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 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).