Jacobi-Maupertuis Randers-Finsler metric for curved spaces and the gravitational magnetoelectric effect
arXiv:1903.11805 · doi:10.1063/1.5098869
Abstract
In this paper we return to the subject of Jacobi metrics for timelike and null geodsics in stationary spactimes, correcting some previous misconceptions. We show that not only null geodesics, but also timelike geodesics are governed by a Jacobi-Maupertuis type variational principle and a Randers-Finsler metric for which we give explicit formulae. The cases of the Taub-NUT and Kerr spacetimes are discussed in detail. Finally we show how our Jacobi-Maupertuis Randers-Finsler metric may be expressed in terms of the effective medium describing the behaviour of Maxwell's equations in the curved spacetime. In particular, we see in very concrete terms how the magnetolectric susceptibility enters the Jacobi-Maupertuis-Randers-Finsler function.
arXiv commentRefrence added
References in corpus (7)
- Gravitational lensing in the Kerr-Randers optical geometry
- Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry
- The Jacobi-metric for timelike geodesics in static spacetimes
- On the energy functional on Finsler manifolds and applications to stationary spacetimes
- Spinoptics in a stationary spacetime
- Jacobi-Maupertuis-Eisenhart metric and geodesic flows
- Geometrical Formulation of Relativistic Mechanics
Cited by in corpus (18)
- Finite-distance gravitational deflection of massive particles by the Kerr-like black hole in the bumblebee gravity model
- Circular orbit of a particle and weak gravitational lensing
- Gravitational deflection of relativistic massive particles by wormholes
- Geometric Approach to Circular Photon Orbits and Black Hole Shadows
- Equivalence of Gibbons-Werner method to geodesics method in the study of gravitational lensing
- Kerr black hole surrounded by a cloud of strings and its weak gravitational lensing in Rastall gravity
- Kerr-Newman-Jacobi geometry and the deflection of charged massive particles
- Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
- Generalized Gibbons-Werner method for stationary spacetimes
- Finite-distance gravitational deflection of massive particles by a rotating black hole in loop quantum gravity
- Deflection of charged signals in a dipole magnetic field in Schwarzschild background using Gauss-Bonnet theorem
- Dynamics in wormhole spacetimes: a Jacobi metric approach
- Harmonic functions and gravity localization
- A Riemannian geometric approach for timelike and null spacetime geodesics
- Mechanics of geodesics in Information geometry and Black Hole Thermodynamics
- More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques
- Deflection of charged massive particles by a four-dimensional charged Einstein-Gauss-Bonnet black hole
- Electromagnetic and gravitational interactions from Lagrangian mechanics