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arXiv · 2305.05501

Algebraic classification of the gravitational field in Weyl-Cartan space-times

Sebastian Bahamonde·Jorge Gigante Valcarcel
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Abstract

We present a complete algebraic classification for the curvature tensor in Weyl-Cartan geometry, by applying methods of eigenvalues and principal null directions on its irreducible decomposition under the group of global Lorentz transformations, thus providing a full invariant characterisation of all the possible algebraic types of the torsion and nonmetricity field strength tensors in Weyl-Cartan space-times. As an application, we show that in the framework of Metric-Affine Gravity the field strength tensors of a dynamical torsion field cannot be doubly aligned with the principal null directions of the Riemannian Weyl tensor in scalar-flat, slowly rotating, stationary and axisymmetric space-times.

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Sebastian Bahamonde, Jorge Gigante Valcarcel. 2023-05-09. Algebraic classification of the gravitational field in Weyl-Cartan space-times. https://doi.org/10.1103/physrevd.108.044037

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