REMARKS ON THE NOTION OF GLOBAL HYPERBOLICITY

Global hyperbolicity is a classical and well-known concept, which lies in the core of General Relativity. Here we discuss briefly five approaches to this concept. They yield different definitions which become natural in diverse contexts: the initial value problem, singularity theorems, existence of maximizing causal geodesics, possibility to split globally the spacetime, causal boundaries. The neat formulation and definitive equivalence between these definitions have been completed only recently. A very brief summary is presented.