Topology Change from Pointlike Sources

In this paper we study topology-changing spacetimes occurring from pointlike sources. Following an old idea of Penrose, we will opt for a non-Hausdorff model of topology change in which an initial pointlike source is "doubled" and allowed to propagate along null rays into an eventual cobordism. By appealing to recent developments in non-Hausdorff differential geometry, we will describe and evaluate gravitational actions on these pointlike topology-changing spacetimes. Motivated by analogous results for the Trousers space, we describe a sign convention for Lorentzian angles that will ensure the dampening of our non-Hausdorff topology-changing spacetimes within a two-dimensional path integral for gravity.