ABSTRACT
The cut locus has played a key role in modern global Riemannian geometry, notably in connection with the Sphere Theorem of Rauch, Klingenberg, and Berger. This chapter considers the analogue of Riemannian cut points for timelike geodesics. The geometric significance of null cut points is similar to that of timelike cut points. The chapter shows how the null cut locus may be applied to prove theorems on the stability of null geodesic incompleteness. The key ideas needed for this application are first, that many physically interesting space–times may be conformally embedded in a portion of the Einstein static universe that is free of null cut points and second, that null cut points are invariant under conformai changes of metric.
