How impossible is topology change?

Abstract

It is often stated that topology change is impossible in classical general relativity. In particular, it appears to be widely believed that the pleasure of topology change comes at a fixed price: topology – changing space times must be singular. This perception is wrong. I discuss here both the kinematics and the dynamics of topology change, in order to clarify what precisely the obstacles are, and (with luck) to dispel a few of the more widespread misconceptions about this process. Some of the work presented here extends the work of Geroch and Tipler to a wider class of spacetimes, and some of it offers novelties – such as an explicit example of non-singular 2-dimensional topology change that have been claimed in the literature to be impossible