More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866929575245643776 |
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| author | Chanda, Sumanto |
| author_facet | Chanda, Sumanto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_06321 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques Chanda, Sumanto General Relativity and Quantum Cosmology Mathematical Physics 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. |
| title | More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques |
| topic | General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/1911.06321 |