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arXiv · 0903.3519

Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric

Erasmo Caponio·Miguel Angel Javaloyes·Antonio Masiello
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Abstract

We show that the index of a lightlike geodesic in a conformally standard stationary spacetime is equal to the index of its spatial projection as a geodesic of a Finsler metric associated to the spacetime. Moreover we obtain the Morse relations of lightlike geodesics connecting a point to an integral line of the standard timelike Killing vector field by using Morse theory on the associated Finsler manifold. To this end, we prove a splitting lemma for the energy functional of a Finsler metric. Finally, we show that the reduction to Morse theory of a Finsler manifold can be done also for timelike geodesics.

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Erasmo Caponio, Miguel Angel Javaloyes, Antonio Masiello. 2009-03-20. Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric. https://doi.org/10.1016/j.anihpc.2010.01.001

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