On the existence of geodesics on stationary Lorentz manifolds with convex boundary

In this paper we consider the problem of the existence and multiplicity for geodesics not touching the boundary of a stationary Lorentz manifold having convex boundary. A physical example of a stationary (and nonstatic) Lorentz manifold having convex boundary is the stationary, axisymmetric, asymptotically flat, gravitational field outside a rotating massive object, whenever its angular speed is small and its mean radius is close to the Schwarzschild radius.