The gauge symmetries of f(R) gravity with torsion in the Cartan formalism

Abstract

First-order general relativity in $n$ dimensions ($n\ge 3$) has an internal gauge symmetry that is the higher-dimensional generalization of three-dimensional local translations. We report the extension of this symmetry for $n$-dimensional f(R) gravity with torsion in the Cartan formalism. The new symmetry arises from the direct application of the converse of Noether's second theorem to the action principle of f(R) gravity with torsion. We show that infinitesimal diffeomorphisms can be written as a linear combination of the new internal gauge symmetry, local Lorentz transformations, and terms proportional to the variational derivatives of the f(R) action. It means that the new internal symmetry together with local Lorentz transformations can be used to describe the full gauge symmetry of f(R) gravity with torsion, and thus diffeomorphisms become a derived symmetry in this setting.

It contains a detailed derivation of the generalization of 3-dimensional "local translations" for 4-dimensional first-order general relativity

References in corpus (2)

• f(R) Gravity with Torsion: The Metric-Affine Approach
• f(R) gravity with torsion: a geometric approach within the J-bundles framework

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