On Fermat's principle for causal curves in time oriented Finsler spacetimes
arXiv:1202.3869 · doi:10.1063/1.4765066
Abstract
In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the secondvariation of the {\it time arrival functional} along a geodesic in terms of the index form associated with the Finsler spacetime Lagrangian. Then the character of the critical points of the time arrival functional is investigated and a Morse index theorem in the context of Finsler spacetime is presented.
20 pages, minor corrections, references added
References in corpus (7)
- Very Special Relativity
- General Very Special Relativity is Finsler Geometry
- Planck-scale modified dispersion relations and Finsler geometry
- Riemann-Finsler geometry and Lorentz-violating kinematics
- Causal structure and electrodynamics on Finsler spacetimes
- Bi-metric pseudo-Finslerian spacetimes
- Some physical displays of the space anisotropy relevant to the feasibility of its being detected at a laboratory
Cited by in corpus (24)
- Resembling dark energy and modified gravity with Finsler-Randers cosmology
- Light cones in Finsler spacetime
- Finsler-Randers Cosmology: dynamical analysis and growth of matter perturbations
- Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions
- Bounce cosmology in generalized modified gravities
- Standard static Finsler spacetimes
- Raychaudhuri equation and singularity theorems in Finsler spacetimes
- Eikonal approximation, Finsler structures, and implications for Lorentz-violating photons in weak gravitational fields
- Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle
- On Finsler spacetimes with a timelike Killing vector field
- On the analyticity of static solutions of a field equation in Finsler gravity
- Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
- On singular generalized Berwald spacetimes and the equivalence principle
- Cosmic magnetization in curved and Lorentz violating space-times
- Volume forms for time orientable Finsler spacetimes
- Maximal acceleration geometries and spacetime curvature bounds
- Multimetric Finsler Geometry
- A variational setting for an indefinite Lagrangian with an affine Noether charge
- On the effect of the maximal proper acceleration in the inertia
- On -jet field approximations to geodesic deviation equations
- A note on Clifford bundles and certain Finsler type spaces
- Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge
- Average of geometric structures in Finsler spaces with Lorentzian signature
- On the Unruh effect for hyperbolic observers in spacetimes of maximal proper acceleration