Journal
GENERAL RELATIVITY AND GRAVITATION
Volume 38, Issue 2, Pages 365-380Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10714-005-0225-6
Keywords
geodesics; variational principle
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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 gamma (worldline of receiver), the lightlike geodesics make the arrival time stationary. Here arrival time refers to a parametrization of the timelike curve gamma. 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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