QM Research Seminar: Topology Change from Pointlike Sources

Speaker: David O'Connell (University of Okinawa)

Abstract:

Topology change is typically modelled by a Lorentz cobordism, which can be seen as a maximal spacelike hypersurface that globally splits into multiple pieces. In this talk we will take the absolute opposite approach, and consider models of topology change in which individual points are duplicated and then allowed to propagate into an eventual cobordism. As we will see, such models are non-Hausdorff, with the Hausdorff-violation occurring along the future nullcones of the duplicated points. Using recent developments in non-Hausdorff differential geometry, we will evaluate the Einstein-Hilbert action on topology changing spacetimes in two dimensions. Interestingly, even in the case of seemingly-flat geometries there will be non-zero curvature contributions coming from Hausdorff-violating submanifolds that sit inside the spacetime. These observations suggest that such spacetimes will generally be suppressed in a path integral that sums over topologies, with more elaborate branching receiving a stronger suppression.