ABSTRACT
We have seen several examples of space-times including those which are also solutions of the Einstein equation. Most of these were local solutions but we also saw extended solutions in the examples of the static black holes. The basic idea of an extension is to embed a given space-time, (M, g), into another one, (M¯, g¯), such that on M ⊂ M¯ , we have g = g¯. The two space-times may be just smooth, or real analytic, or solutions of the Einstein equation. If no such extension is possible, the space-time is said to be in-extendable. The focus of this chapter is on in-extendable space-times. Eventually we would like such space-times as solutions of the Einstein equation with suitable matter stress tensor, but to begin with we just focus on candidate space-times.
