  In order to apply variational methods to the action functional for geodesics
of a stationary spacetime, some hypotheses, useful to obtain classical
Palais-Smale condition, are commonly used: pseudo-coercivity, bounds on certain
coefficients of the metric, etc. We prove that these technical assumptions
admit a natural interpretation for the conformal structure (causality) of the
manifold. As a consequence, any stationary spacetime with a complete timelike
Killing vector field and a complete Cauchy hypersurface (thus, globally
hyperbolic), is proved to be geodesically connected.
