On Fermat's principle for causal curves in time oriented Finsler spacetimes
arXiv:1202.3869 · doi:10.1063/1.4765066
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.
20 pages, minor corrections, references added