2007/12/31 by E. Minguzzi · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Causal sets #Causal structure #Fixed Point Theorems Analysis #Geometric Analysis and Curvature Flows #Imprisonment #Invariant (physics) #Property (philosophy) #Spacetime #gr-qc
paper · pdf · doi:10.1063/1.2937907
published as J.Math.Phys.49:062503,2008 · 12 pages, 2 figures. v2: improved results on totally imprisoned curves, a figure changed, some misprints fixed
arxiv created 2008/05/12 · openalex publication_date 2008/06/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The non-imprisonment conditions on spacetimes are studied. It is proved that the non-partial imprisonment property implies the distinction property. Moreover, it is proven that feeble distinction, a property which stays between weak distinction and causality, implies non-total imprisonment. As a result the non-imprisonment conditions can be included in the causal ladder of spacetimes. Finally, totally imprisoned causal curves are studied in detail, and results concerning the existence and properties of minimal invariant sets are obtained.