Institute of Mathematics


Modul:   MAT074  Talks in mathematical physics

Topology Change from Pointlike Sources

Talk by David O'Connell

Date: 20.11.23  Time: 13.15 - 14.15  Room: Y27H25

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 necessarily non-Hausdorff, with the Hausdorff-violation occurring along the future nullcones of the duplicated points. Through recent developments in non-Hausdorff differential geometry, we will evaluate the Einstein-Hilbert action on topology changing spacetimes in two dimensions. We will see that even in the case of seemingly-flat geometries, there may be non-zero curvature contributions coming from the Hausdorff-violating submanifolds that sit inside the spacetime. We will then conclude with some observations that mirror a famous discussion of Sorkin and Louko regarding complex metrics and suppression in path integrals.