During the past years there has been a considerable amount of research related to the problem of geodesic connectedness of Lorentzian manifolds. In particular, some geometric sufficient conditions have been introduced so that stationary space-times, i.e. spacetimes equiped with a timelike Killing vector field, are geodesically connected. Recently, we characterized geodesically connected points in a spacetime equiped with a lightlike Killing vector field.
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