0903.3519 (Erasmo Caponio et al.)

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

Erasmo Caponio, Miguel Angel Javaloyes, Antonio Masiello

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.

View original: http://arxiv.org/abs/0903.3519