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2019

(Non-)uniqueness of Einstein-Palatini Gravity

Janssen, Bert, Jimenez-Cano, Alejandro, Orejuela, Jose Alberto et al.

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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.

(Non-)uniqueness of Einstein-Palatini Gravity · Around

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J. D. McCrea. Irreducible decompositions of nonmetricity, torsion, curvature and Bianchi identities in metric-affine spacetimes
1992
Earlier work this paper cites.
S. Deser. Inequivalence of first and second-order formulations in d = 2 d=2 gravity models
1996
Earlier work this paper cites.
H. Kleinert and A. Pelster. Letter: Autoparallels from a New Action Principle
1999
Earlier work this paper cites.

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F. W. Hehl and Y. N. Obukhov. Elie Cartan’s torsion in geometry and field theory, an essay
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M. Borunda, B. Janssen and M. Bastero-Gil. Palatini versus metric formulation in higher curvature gravity
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Then

N. Dadhich and J.M. Pons. On the equivalence of the Einstein-Hilbert and the Einstein-Palatini formulations of general relativity for an arbitrary connection
Original
2012
Later among the works it cites.
A. N. Bernal, B. Janssen, A. Jiménez-Cano, J. A. Orejuela, M. Sánchez and P. Sánchez-Moreno. On the (non-)uniqueness of the Levi-Civita solution in the Einstein-Hilbert-Palatini formalism
Original
2017
Later among the works it cites.

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