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

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.

AMSLaTeX, 22 pages. v5: Appendix B removed and replaced by arXiv:1211.3071 [math.DG]

References in corpus (3)

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• On the energy functional on Finsler manifolds and applications to stationary spacetimes
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