Metric-affine variational principles in general relativity. I. Riemannian space-time

Hehl, Friedrich W.; Kerlick, G. David

doi:10.1007/bf00760141

Cited by 116 publications

(127 citation statements)

References 18 publications

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“…The use of the Lagrange multipliers in theories of gravity has been studied in Refs. [20,25,26]. For the sake of simplicity, we rewrite the Lagrangian density L g as…”

Section: Field Equationsmentioning

confidence: 99%

Stability in quadratic torsion theories

et al. 2017

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We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier.

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“…The use of the Lagrange multipliers in theories of gravity has been studied in Refs. [20,25,26]. For the sake of simplicity, we rewrite the Lagrangian density L g as…”

Section: Field Equationsmentioning

confidence: 99%

Stability in quadratic torsion theories

et al. 2017

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“…In the last few years new attempts [1] - [3] have been made to revive the ideas of Weyl [4], [? ] for using manifolds with independent affine connection and metric (spaces with affine connection and metric) as a model of space-time in the theory of gravitation [3].…”

Section: Space-time Geometry and Differential Geometrymentioning

confidence: 99%

“…The description of the gravitational interaction and its unification with the other types of interactions over differentiable manifolds with affine connections and metric [(L n , g)-spaces] induces [1] the introduction of an affine connection with a corresponding covariant differential operator s ∇ ξ constructed by means of ∇ ξ and Q ξ in the form…”

mentioning

confidence: 99%

Spaces with contravariant and covariant affine connections and metrics

Manoff¹

1999

Phys. Part. Nucl.

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“…This statement can be generalized to theories of gravitation with Lagrangians that depend on the full Ricci tensor and the second Ricci tensor [20,21], and to a general connection with torsion [21]. There also exist formulations of gravity in which the dynamical variables are: metric and torsion (Einstein-Cartan theory) [22,23,24,25,26,27], metric and nonsymmetric connection [28,29], tetrad and spin connection (EinsteinCartan-Kibble-Sciama theory) [30,31,32,33,34,35,36], spin connection [37,38,39], and spinors [40,41].…”

Section: Introductionmentioning

confidence: 99%