  Changing the topology has changed the mathematics of the situation in two ways, which tend to pull in opposite directions. On the one hand, S is no longer a Cauchy surface, so it is perhaps not surprising that data on S do not suffice to fix a unique global solution. But on the other hand, there is an added constraint: data “coming out” of L− must exactly match data “going in” to L+, even though what comes out of L− helps to determine what goes into L+. This added consistency constraint tends to cut down on solutions, although in this case the additional constraint is more than outweighed by the freedom to consider various sorts of data on L+/L-.