General Relativity and Gravitation

, Volume 38, Issue 2, pp 365–380 | Cite as

Fermat principle in Finsler spacetimes

  • Volker Perlick
Research Article


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 q (emission event) to a timelike curve γ (worldline of receiver), the lightlike geodesics make the arrival time stationary. Here “arrival time” refers to a parametrization of the timelike curve γ. 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.


Geodesics Variational principle 


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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.TU BerlinBerlinGermany

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