Globally hyperbolic space-time which are timelike Cauchy complete

Let M be a globally hyperbolic manifold. Among the many forms of completeness that may be imposed on M are timelike Cauchy completeness and finite compactness. These two forms of completeness are shown to be equivalent for globally hyperbolic manifolds. They are also equivalent to the statement that every inextendible future-directed (past-directed) geodesic starting in the chronological future (past) of p has points at arbitrarily large distance from p. (author)