Globally noncausal space-times

It is proved that if there is a naked singularity, then there will be some null geodesic, reaching I+ from the singularity, which does not satisfy the strong curvature condition regardless of whether causality is violated or not. Assuming that a naked singularity is a strong curvature singularity only sufficiently far to the future, it is proved that strong causality is violated arbitrarily close to I+. (author)