ABSTRACT
This chapter discusses extensions and local extensions of space–times. It recalls that the class of globally hyperbolic space–times possesses this useful property. The chapter considers forms of completeness such as nonspacelike geodesic completeness, bounded acceleration completeness, and bundle completeness that have been studied in singularity theory in general relativity, G. F. R. Ellis and B. G. Schmidt. It describes the Schmidt b-boundary and the Geroch–Kronheimer–Penrose causal boundary. The chapter also recalls that for arbitrary Lorentzian manifolds, geodesic completeness does not imply the existence of maximal geodesic segments joining causally related pairs of points. It also discusses the important and useful fact that distance realizing geodesics do exist for the class of globally hyperbolic space–times. The chapter defines extendibility and inextendibility of Lorentzian manifold.
