More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques

Abstract

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.

arXiv comment24 pages, any comments are welcome

References in corpus (32)

• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• Finsler geometric extension of Einstein gravity
• Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• The Jacobi-metric for timelike geodesics in static spacetimes
• Finsler spacetime geometry in Physics
• Embedding Galilean and Carrollian geometries I. Gravitational waves
• The finite-distance gravitational deflection of massive particles in stationary spacetime: a Jacobi metric approach
• Cosmological aspects of the Eisenhart-Duval lift
• Jacobi-Maupertuis-Eisenhart metric and geodesic flows
• Embedding nonrelativistic physics inside a gravitational wave
• Schwarzschild-like solutions in Finsler-Randers gravity
• Jacobi-Maupertuis Randers-Finsler metric for curved spaces and the gravitational magnetoelectric effect
• Generalised Eisenhart lift of the Toda chain
• Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
• Classical aspects of lightlike dimensional reduction
• Kerr-Newman-Jacobi geometry and the deflection of charged massive particles
• Conformal Killing Tensors and covariant Hamiltonian Dynamics
• The Eisenhart Lift for Field Theories
• Ricci-flat spacetimes admitting higher rank Killing tensors
• Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
• Applications of the Schwarzschild-Finsler-Randers model
• Eisenhart lift for higher derivative systems
• Jacobi-Maupertius metric and Kepler equation
• Randers pp-waves
• Geometry of the isotropic oscillator driven by the conformal mode
• On the Jacobi metric for a general Lagrangian system
• Geometrical Formulation of Relativistic Mechanics
• Eisenhart lift of Koopman-von Neumann mechanics
• Hawking radiation in a non-covariant frame: the Jacobi metric approach
• Eisenhart Lift of $2$--Dimensional Mechanics
• Self-dual metrics with maximally superintegrable geodesic flows