Null cut loci of spacelike surfaces |
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Authors: | Demir N. Kupeli |
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Affiliation: | (1) Department of Mathematics, University of Alabama at Birmingham, 35294 Birmingham, Alabama;(2) Present address: Department of Mathematics, SUNY at Stony Brook, 11994 Stony Brook, New York |
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Abstract: | The null cut locus of a spacelike submanifold of codimension 2 in a space-time is defined. In globally hyperbolic space-times, it is shown that the future (past) null cut locuscn+(H) [cn-(H)] of a compact, acausal, spacelike submanifoldH of codimension 2 is a closed subset of the space-time, and each pointx cn+(H) is either a focal point ofH along some future-directed null geodesic meetingH orthogonally or there exist at least two null geodesics fromH tox, realizing the distance betweenH andx or both. Also, it can be shown that the assumptions of the Penrose's singularity theorem for open globally hyperbolic space-times may be weakened to the space-times which are conformal to an open subset of an open globally hyperbolic space-time.This study is based on Chapter 3 of the author's Ph.D. thesis. |
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