Chronological null complete spacetimes admit a global time

TL;DR

This paper proves that chronological spacetimes which are null geodesically complete and satisfy certain energy and genericity conditions admit a global time function, ensuring stable causality.

Contribution

It establishes that null geodesic completeness combined with null energy and genericity conditions guarantees the existence of a global time function in chronological spacetimes.

Findings

Chronological spacetimes without lightlike lines are stably causal.

Null geodesic completeness and energy conditions imply the existence of a time function.

The result connects causal stability with geometric and physical conditions.

Abstract

The result "chronological spacetimes without lightlike lines are stably causal" is announced and motivated. It implies that chronological spacetimes which are null geodesically complete and satisfy the null genericity and the null (averaged) energy condition admit a time function.