Globally Hyperbolic Spacetimes Can be Defined as “ Causal ” Instead of “ Strongly Causal ” Antonio

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 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. 2000 MSC: Primary 53C50, Secondary 53C80, 83C75.