Globally hyperbolic spacetimes can be defined as ‘causal’ instead of ‘strongly causal’

Abstract

The classical definition of global hyperbolicity for a spacetime (M, g) comprises two conditions: (A) compactness of the diamonds J+(p)∩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 requirements on the spacetime in the classical definition of causal simplicity (i.e. to be distinguishing plus the closedness of J+(p), J−(q)) can be weakened by requiring only to be 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.