Causality conditions and the lengths of nonspacelike curves |
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Authors: | S V Dhurandhar P S Joshi |
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Institution: | (1) Raman Research Institute, 560 006 Bangalore, India;(2) Tata Institute of Fundamental Research, 400 005 Bombay, India |
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Abstract: | In globally hyperbolic space-times there is a finite upper bound on the proper time lengths of nonspacelike curves between two chronologically related events. We show that if global hyperbolicity is replaced by a weaker causality condition, then there can exist chronologically related events in the space-time such that the proper time lengths of nonspacelike curves joining them grow without bound. We also show that the existence of a finite upper bound on the lengths of nonspacelike curves between two chronologically related events implies only chronology of the space-time but not causality. |
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