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arXiv · 1202.3869

On Fermat's principle for causal curves in time oriented Finsler spacetimes

Ricardo Gallego Torromé·Paolo Piccione·Henrique Vitório
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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.

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Ricardo Gallego Torromé, Paolo Piccione, Henrique Vitório. 2012-02-17. On Fermat's principle for causal curves in time oriented Finsler spacetimes. https://doi.org/10.1063/1.4765066

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