(Non-)uniqueness of Einstein-Palatini Gravity

Abstract

We analyse the most general connection allowed by Einstein-Hilbert theory in Palatini formalism. We also consider a matter lagrangian independent of the affine connection. We show that any solution of the equation of the connection is essentially Levi-Civita up to a term that contains an undetermined 1-form. Finally, it is proved that these connections and Levi-Civita describe a completely equivalent physics.

arXiv comment8 pages, 2 figures. Talk given by A.J.C. at the workshop Frontiers of Fundamental Physics 15 (Orihuela, Spain, November 2017)

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Cited by in corpus (5)

• Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar
• Geometric inequivalence of metric and Palatini formulations of General Relativity
• On the topological character of metric-affine Lovelock Lagrangians in critical dimensions
• A non-trivial connection for the metric-affine Gauss-Bonnet theory in $D=4$
• Asymptotically Safe Hilbert-Palatini Gravity in an On-Shell Reduction Scheme