Chronological Spacetimes without Lightlike Lines are Stably Causal

2008/06/01 by E. Minguzzi · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Relativity and Gravitational Theory #gr-qc

paper · pdf · doi:10.1007/s00220-009-0784-6

published as Commun.Math.Phys.288:801-819,2009 · 20 pages, 6 figures

arxiv created 2008/06/01 · openalex publication_date 2009/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

The statement of the title is proved. It implies that under physically reasonable conditions, spacetimes which are free from singularities are necessarily stably causal and hence admit a time function. Read as a singularity theorem it states that if there is some form of causality violation on spacetime then either it is the worst possible, namely violation of chronology, or there is a singularity. The analogous result: "Non-totally vicious spacetimes without lightlike rays are globally hyperbolic" is also proved, and its physical consequences are explored.

Citations

• Domain of Dependence
• Singularity Theorems and Their Consequences
• The singularities of gravitational collapse and cosmology
• Weak distinction and the optimal definition of causal continuity
• The causal ladder and the strength of K -causality: II

Cited by

• ON THE GLOBAL EXISTENCE OF TIME