On the Regularity Implied by the Assumptions of Geometry

Explore a 46-minute conference talk on the theory of Regularity Transformation (RT) equations, presented by Moritz Reintjes at the Workshop on "Non-regular Spacetime Geometry" held at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into an elliptic system of partial differential equations that determines coordinate and gauge transformations to remove apparent singularities in spacetime by establishing optimal regularity for general connections. Discover how this theory extends the optimal regularity result of Kazdan-DeTurck and the compactness theorem of Uhlenbeck from Riemannian to Non-Riemannian geometry. Learn about its applications in General Relativity, including the resolution of an open problem regarding the non-singularity of Lorentzian metrics in shock wave solutions of Einstein-Euler equations. Gain insights into the existence of geodesic curves, locally inertial coordinates, and the Newtonian limit in a classical sense for these solutions.