# Torsion/nonmetricity duality in f(R) gravity

@article{Iosifidis2019TorsionnonmetricityDI, title={Torsion/nonmetricity duality in f(R) gravity}, author={Damianos Iosifidis and Anastasios C. Petkou and Christos G. Tsagas}, journal={General Relativity and Gravitation}, year={2019}, volume={51}, pages={1-15} }

Torsion and nonmetricity are inherent ingredients in modifications of Eintein’s gravity that are based on affine spacetime geometries. In the context of pure f(R) gravity we discuss here, in some detail, the relatively unnoticed duality between torsion and nonmetricity. Our novel suggestion is that torsion and nonmetricity are physically equivalent properties of spacetimes having nontrivial Weyl structure. Our main example is $$R^2$$R2 gravity where torsion and nonmetricity are related by…

## 28 Citations

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Pure $R^2$ gravity has been shown to be equivalent to Einstein gravity with non-zero cosmological constant and a massless scalar field. We show that the Palatini formulation of pure $R^2$ gravity is…

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Einstein–Cartan theory is an extension of the standard formulation of General Relativity where torsion (the antisymmetric part of the affine connection) is non-vanishing. Just as the space-time…

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- MathematicsClassical and Quantum Gravity
- 2019

This article presents a systematic way to solve for the affine connection in metric-affine geometry. We start by adding to the Einstein–Hilbert action, a general action that is linear in the…

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