K-causality and degenerate spacetimes

The causal relation K+ was introduced by Sorkin and Woolgar to extend the standard causal analysis of C-2 spacetimes to those that are only C-0. Most of their results also hold true in the case of metrics with degeneracies which are C-0 but vanish at isolated points. In this paper we seek to examine K+ explicitly in the case of topology-changing 'Morse histories' which contain degeneracies. We first demonstrate some interesting features of this relation in globally Lorentzian spacetimes. In particular, we show that K+ is robust and the Hawking and Sachs characterization of causal continuity translates into a natural condition in terms of K+. We then examine K+ in topology-changing Morse spacetimes with the degenerate points excised and then for the Morse histories in which the degenerate points are reinstated. We find further characterizations of causal continuity in these cases.