Fermat Principle in Finsler Spacetimes

TL;DR

This paper demonstrates that in Finsler spacetimes with Lorentzian signature, lightlike geodesics follow a variational principle where they make the arrival time stationary among all lightlike curves connecting an emission point to a receiver's worldline.

Contribution

It establishes a Fermat principle for lightlike geodesics in Finsler Lorentzian manifolds, extending classical results to anisotropic and alternative spacetime models.

Findings

Lightlike geodesics satisfy a stationary arrival time principle.

Applicable to Finsler-based vacuum light rays and anisotropic media.

Provides a variational framework for light propagation in generalized spacetimes.

Abstract

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.