Palatini Formalism
Palatini may refer to: * Attilio Palatini (1889–1949), Italian mathematician * (1855–1914), Italian politician * Palatini identity * Palatini variation * Latin plural of Palatine A palatine or palatinus (in Latin; plural ''palatini''; cf. derivative spellings below) is a high-level official attached to imperial or royal courts in Europe since Roman times.

Attilio Palatini
Attilio Palatini (18 November 1889 – 24 August 1949) was an Italian mathematician born in Treviso. Biography Palatini was the seventh of the eight children of Michele (1855-1914) and Ilde Furlanetto (1856-1895). In 1900, during the celebrations for the election of his father to Parliament, he was blinded by a young man from Treviso, losing the use of one eye. He completed his secondary studies in Treviso. He graduated in mathematics in 1913 at the University of Padua, where he was a student of Ricci-Curbastro and of Levi-Civita. He taught rational mechanics at the Universities of Messina, Parma and Pavia. He was mainly involved in absolute differential calculus and in general relativity. Within this latter subject he gave a sound generalization of the variational principle. In 1919, Palatini wrote an important article where he proposed a new approach to the variational formulation of Einstein's gravitational field equations. In the same paper, Palatini also showed that the ...
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Palatini Identity
In general relativity and tensor calculus, the Palatini identity is: : \delta R_ = \nabla_\rho (\delta \Gamma^\rho_) - \nabla_\nu (\delta \Gamma^\rho_), where \delta \Gamma^\rho_ denotes the variation of Christoffel symbols and \nabla_\rho indicates covariant differentiation. A proof can be found in the entry Einstein–Hilbert action. The "same" identity holds for the Lie derivative \mathcal_ R_. In fact, one has: : \mathcal_ R_ = \nabla_\rho (\mathcal_ \Gamma^\rho_) - \nabla_\nu (\mathcal_ \Gamma^\rho_), where \xi = \xi^\partial_ denotes any vector field on the spacetime manifold M. See also * Einstein–Hilbert action *Palatini variation *Ricci calculus * Tensor calculus *Christoffel symbols *Riemann curvature tensor In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common way used to express the curvature of Riemannian manifolds ... N ...
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Palatini Variation
In general relativity and gravitation the Palatini variation is nowadays thought of as a variation of a Lagrangian (field theory), Lagrangian with respect to the connection. In fact, as is well known, the Einstein–Hilbert action for general relativity was first formulated purely in terms of the Metric tensor (general relativity), spacetime metric . In the Palatini variational method one takes as independent field variables not only the ten components but also the forty components of the affine connection , assuming, a priori, no dependence of the from the and their derivatives. The reason the Palatini variation is considered important is that it means that the use of the Affine connection, Christoffel connection in general relativity does not have to be added as a separate assumption; the information is already in the Lagrangian. For theories of gravitation which have more complex Lagrangians than the Einstein–Hilbert action, Einstein–Hilbert Lagrangian of general relativi ...
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Palatine
A palatine or palatinus (in Latin; plural ''palatini''; cf. derivative spellings below) is a high-level official attached to imperial or royal courts in Europe since Roman times."Palatine"
From the ''

Oxford English Dictionary

''. Retrieved November 19, 2008. The term ''palatinus'' was first used in for