Existence of geodesics in static Lorentzian manifolds with convex boundary
Published online by Cambridge University Press: 11 July 2007
Abstract
We study some global geometric properties of a static Lorentzian manifold Λ embedded in a differentiable manifold M, with possibly non-smooth boundary ∂Λ. We prove a variational principle for geodesics in static manifolds, and using this principle we establish the existence of geodesics that do not touch ∂Λ and that join two fixed points of Λ. The results are obtained under a suitable completeness assumption for Λ that generalizes the property of global hyperbolicity, and a weak convexity assumption on ∂Λ. Moreover, under a non-triviality assumption on the topology of Λ, we also get a multiplicity result for geodesics in Λ joining two fixed points.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 1 , February 2000 , pp. 189 - 215
- Copyright
- Copyright © Royal Society of Edinburgh 2000
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