Normal geodesics connecting two non-necessarily spacelike submanifolds in a stationary spacetime

Details Normal geodesics connecting two non-necessarily spacelike submanifolds in a stationary spacetime Normal geodesics connecting two non-necessarily spacelike submanifolds in a stationary spacetime

2009-02-16

arxiv.org/abs/0902.2754v3

Adv. Nonlinear Stud., 10 (2010) 851--866

Mathematics

Differential Geometry

Minor revision; 16 pages

Scientific paper

In this paper we obtain an existence theorem for normal geodesics joining two given submanifolds in a globally hyperbolic stationary spacetime. The proof is based on both variational and geometric arguments involving the causal structure of the spacetime, the completeness of suitable Finsler metrics associated to it and some basic properties of a submersion. By this interaction, unlike previous results on the topic, also non--spacelike submanifolds can be handled.

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