Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-12-23
J.Math.Phys.49:092501,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages, 1 figure. v2: Misprints fixed, matches published version
Scientific paper
10.1063/1.2973048
The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the beginning are one, two or at most denumerable. Some applications are considered. It is proved that in chronological spacetimes, strong causality is either everywhere verified or everywhere violated on maximizing lightlike segments with open domain. As a consequence, if in a chronological spacetime two distinct lightlike lines intersect each other then strong causality holds at their points. Finally, it is proved that two distinct components of the chronology violating set have disjoint closures or there is a lightlike line passing through each point of the intersection of the corresponding boundaries.
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