https://doi.org/10.1140/epjp/s13360-024-05775-y
Regular Article
More on Jacobi metric: Randers–Finsler metrics, frame dragging and geometrisation techniques
Indian Institute of Astrophysics, Block 2, 100 Feet Road, Koramangala, 560034, Bengaluru, Karnataka, India
Received:
14
July
2024
Accepted:
24
October
2024
Published online:
7
November
2024
In this article, I demonstrate a new method to derive Jacobi metrics from Randers–Finsler metrics by introducing a more generalised approach to Hamiltonian mechanics for such spacetimes and discuss the related applications and properties. I introduce Hamiltonian mechanics with the constraint for relativistic momentum, including a modification for null curves and two applications as exercises: derivation of a relativistic harmonic oscillator and analysis of Schwarzschild Randers–Finsler metric. Then I describe the main application for constraint mechanics in this article: a new derivation of Jacobi metric for time-like and null curves, comparing the latter with optical metrics. After that, I discuss frame dragging with the Jacobi metric and two applications for Randers–Finsler metrics: an alternative to Eisenhart lift, and different metrics that share the same Jacobi metric.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
