Geodesics with prescribed energy on static Lorentzian manifolds with convex boundary

By using some variational principles and the Ljusternik-Schnirelmann critical point theory, we extend some previous results dealing with the existence and multiplicity of geodesics having prescribed energy joining a point with a line on static Lorentzian manifolds with convex boundary. Our techniques work also in the case of timelike and spacelike geodesics on manifolds with boundary and for a physically relevant class of spacetimes with non-smooth boundary. (C) 2000 Elsevier Science B.V. All rights reserved.