  This paper clarifies some aspects of Lorentzian topology change, and it
extends to a wider class of spacetimes previous results of Geroch and Tipler
that show that topology change is only to be had at a price. The scenarios
studied here are ones in which an initial spacelike surface is joined by a
connected ``interpolating spacetime'' to a final spacelike surface, possibly of
different topology. The interpolating spacetime is required to obey a condition
called causal compactness, a condition satisfied in a very wide range of
situations. No assumption is made about the dimension of spacetime. First, it
is stressed that topology change is kinematically possible; i.e., if a field
equation is not imposed, it is possible to construct topology-changing
spacetimes with non-singular Lorentz metrics. Simple 2-dimensional examples of
this are shown. Next, it is shown that there are problems in such spacetimes:
Geroch's closed-universe argument is applied to causally compact spacetimes to
show that even in this wider class of spacetimes there are causality violations
associated with topology change. It follows from this result that there will be
causality violations if the initial (or the final) surface is not connected,
even when there is no topology change. Further, it is shown that in dimensions
$\geq 3$ causally compact topology-changing spacetimes cannot satisfy
Einstein's equation (with a reasonable source); i.e., there are severe
dynamical obstructions to topology change. This result extends a previous one
due to Tipler. Like Tipler's result, it makes no assumptions about geodesic
completeness; i.e., it does not permit topology change even at the price of
singularities (of the standard incomplete-geodesic variety). Brief discussions
are also given of ways in which the results of this paper might be
circumvented.
