ABSTRACT
This chapter explores geodesic connectedness from a general viewpoint and related to geodesic pseudoconvexity and geodesic disprisonment. It recalls that the space-times have been known at least since Penrose to fail to be globally hyperbolic; thus we may not use the existence of maximal nonspacelike geodesic segments in this proof. The exact plane wave solutions then arise as simplified models for this phenomenon, compromising between reality and complexity to paraphrase Misner, Thorne, and Wheeler. The “unbounded” nature of this one-parameter family of geodesics precludes the geodesic system from being pseudoconvex, and also prevents this class of space-times from being globally hyperbolic. Requirement serves to ensure that in a certain Prufer type transformation for the solution of the O.D.E., a continuous determination of arctan may be made.
