2007/12/31 by E. Minguzzi
Mathematics · Physics and Astronomy · #Almost everywhere #Black Holes and Theoretical Physics #Causality (physics) #Countable set #Disjoint sets #Domain (mathematical analysis) #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Intersection (aeronautics) #Limit (mathematics) #Limit point #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum mechanics #gr-qc
paper · pdf · doi:10.1063/1.2973048
published as J.Math.Phys.49:092501,2008 · 25 pages, 1 figure. v2: Misprints fixed, matches published version
openalex publication_date 2008/09/01 · arxiv created 2008/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.