Convexity conditions on the boundary of a stationary spacetime and applications

We deal with the convexity of the boundary of a standard stationary spacetime L = M x R. We obtain a characterization of this notion by means of Riemannian conditions involving a potential plus a magnetic field on M, where both are linked to the coefficients of the metric. Natural applications of our results concern geodesics having a prescribed parametrization proportional to the arc length, joining a point to a line and periodic, on non-complete manifolds, and in particular on Kerr spacetime.