Chronological spacetimes without lightlike lines are stably causal

TL;DR

This paper proves that chronological spacetimes without lightlike lines are stably causal, implying non-singular, causally well-behaved spacetimes admit a time function, and establishes a link between causality violations and singularities.

Contribution

It introduces new theorems connecting the absence of lightlike lines to stable causality and explores their physical implications, including a singularity theorem.

Findings

Chronological spacetimes without lightlike lines are stably causal.

Spacetimes free from singularities are necessarily stably causal.

Causality violations imply the presence of singularities or extreme causality violations.

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.