Singularities in nonsimply connected space–times

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Abstract
Space–times with asymptotically flat nonsimply connected spacelike slices are shown to possess enough intrinsic geometric structure to guarantee the existence of singularities under conditions usually considered insufficient. In particular, it is shown that if the normal geodesics to the spacelike slice are converging on a suitable compact set, and the space–time satisfies a standard energy condition, then it is timelike geodesically incomplete. A similar result holds if the space–time satisfies the chronology and generic conditions.

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