Existence of geodesics in static Lorentzian manifolds with convex boundary

We study some global geometric properties of a static Lorentzian manifold L ambda embedded in a differentiable manifold M, with possibly non-smooth bou ndary partial derivative Lambda. We prove a variational principle for geode sics in static manifolds, and using this principle we establish the existen ce of geodesics that do not touch partial derivative Lambda and that join t wo fixed points of Lambda. The results are obtained under a suitable comple teness assumption for Lambda that generalizes the property of global hyperb olicity, and a weak convexity assumption on partial derivative Lambda. More over, under a non-triviality assumption on the topology of Lambda, we also get a multiplicity result for geodesics in Lambda joining two fixed points.