Fermat Principle in Finsler Spacetimes

Details Fermat Principle in Finsler Spacetimes Fermat Principle in Finsler Spacetimes

2005-08-08

arxiv.org/abs/gr-qc/0508029v1

Gen.Rel.Grav. 38 (2006) 365-380

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, submitted to Gen. Rel. Grav

Scientific paper

10.1007/s10714-005-0225-6

It is shown that, on a manifold with a Finsler metric of Lorentzian signature, the lightlike geodesics satisfy the following variational principle. Among all lightlike curves from a point (emission event) to a timelike curve (worldline of receiver), the lightlike geodesics make the arrival time stationary. Here ``arrival time'' refers to a parametrization of the timelike curve. This variational principle can be applied (i) to the vacuum light rays in an alternative spacetime theory, based on Finsler geometry, and (ii) to light rays in an anisotropic non-dispersive medium with a general-relativistic spacetime as background.

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