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.

Limit curve theorems in Lorentzian geometry / Minguzzi, Ettore. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 49:(2008), pp. 092501-092501-18. [10.1063/1.2973048]

Limit curve theorems in Lorentzian geometry

MINGUZZI, ETTORE
2008

Abstract

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.
2008
49
092501
092501-18
Minguzzi, Ettore
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/320518
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