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arXiv · 1209.3596

Differential geometry, Palatini gravity and reduction

Santiago Capriotti
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Abstract

The present article deals with a formulation of the so called (vacuum) Palatini gravity as a general variational principle. In order to accomplish this goal, some geometrical tools related to the geometry of the bundle of connections of the frame bundle $LM$ are used. A generalization of Lagrange-Poincaré reduction scheme to these types of variational problems allows us to relate it with the Einstein-Hilbert variational problem. Relations with some other variational problems for gravity found in the literature are discussed.

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Santiago Capriotti. 2013-11-29. Differential geometry, Palatini gravity and reduction. https://doi.org/10.1063/1.4862855

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