Globally hyperbolic spacetimes can be defined as "causal" instead of "strongly causal"

TL;DR

This paper demonstrates that the classical definition of global hyperbolicity in spacetimes can be simplified by replacing the strong causality condition with the weaker causality condition, refining the causal hierarchy.

Contribution

It shows that global hyperbolicity can be characterized using only causality instead of strong causality, simplifying the causal conditions needed.

Findings

Strong causality can be replaced by causality in defining global hyperbolicity.

Causal simplicity can be weakened from distinguishing to causal.

The causal ladder's consistency supports the new characterization.

Abstract

The classical definition of {\em global hyperbolicity} for a spacetime $(M,g)$ comprises two conditions: (A) compactness of the diamonds $J^+(p)\cap J^-(q)$, and (B) strong causality. Here we show that condition (B) can be replaced just by causality. In fact, we show first that the classical definition of causal simplicity (which impose to be distinguishing, apart from the closedness of $J^+(p)$, $J^-(q)$) can be weakened in causal instead of distinguishing. So, the full consistency of the causal ladder (recently proved by the authors in a definitive way) yields directly the result.