Chronological spacetimes without lightlike lines are stably causal

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.

20 pages, 6 figures

References in corpus (5)

• The causal hierarchy of spacetimes
• Limit curve theorems in Lorentzian geometry
• The causal ladder and the strength of K-causality. II
• Non-imprisonment conditions on spacetime
• Weak distinction and the optimal definition of causal continuity

Cited by in corpus (1)

• Widening the light cones on subsets of spacetime: some variations to stable causality