Periodic trajectories on stationary Lorentzian manifolds

An existence and multiplicity result for periodic trajectories on stationary Lorentzian manifolds, possibly with boundary, whose proof is based on a Morse theory approach is presented. A Lorentzian manifold is a smooth connected finite-dimensional manifold M equipped with a (0,2) tensor field g such that for any z∈M g(z) [·,·] is a nondegenerate symmetric bilinear form on the tangent space TzM having exactly one negative eigenvalue. Moreover, relativistic spacetimes are a particular class of Lorentzian manifolds of dimension four.