Report
On the Finsler variational nature of autoparallels in metric-affine geometry
| Τίτλος: | On the Finsler variational nature of autoparallels in metric-affine geometry |
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| Συγγραφείς: | Csillag, Lehel, Voicu, Nicoleta, Elgendi, Salah, Pfeifer, Christian |
| Έτος έκδοσης: | 2026 |
| Συλλογή: | Mathematical Physics General Relativity and Quantum Cosmology |
| Θεματικοί όροι: | Mathematical Physics, General Relativity and Quantum Cosmology, Differential Geometry |
| Περιγραφή: | In metric-affine geometry, autoparallels are generically non-variational, i.e., they are not the extremals of any action integral. The existence of a parametrization-invariant action principle for autoparallels is a long-standing open problem, which is equivalent to the so-called Finsler metrizability of the connection -- that is, to the fact that these autoparallels can be interpreted as Finsler geodesics. In this article, we address this problem for the class of torsion-free affine connections with vectorial nonmetricity, which includes, as notable subcases, Weyl and Schrödinger connections. For this class, we determine the necessary and sufficient conditions for the existence of a Finsler Lagrangian that metrizes the connection (and depends only algebraically on the metric and on the nonmetricity defining vector field). In the cases where such a Finsler Lagrangian exists, we construct it explicitly. In particular, we show that a broad class of such connections is in fact Finsler metrizable, i.e., the autoparallels of these connections are Finsler geodesics. 23 pages |
| Τύπος εγγράφου: | Working Paper |
| DOI: | 10.48550/arXiv.2603.18416 |
| Σύνδεσμος πρόσβασης: | https://arxiv.org/abs/2603.18416 |
| Αριθμός Καταχώρησης: | edsarx.2603.18416 |
| Βάση Δεδομένων: | arXiv |
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