Globally hyperbolic spacetimes can be defined without the 'causal' condition

Understand

Reasonable spacetimes are non-compact and of dimension larger than two.

• We show that these spacetimes are globally hyperbolic if and only if the causal diamonds are compact.
• That is, there is no need to impose the causality condition, as it can be deduced.
• We also improve the definition of global hyperbolicity for the non-regular theory (non $C^{1,1}$ metric) and for general cone structures by proving the following convenient characterization for upper semi-continuous cone distributions: causality and the causally convex hull of compact sets is compact.