A Nonsmooth Approach to Einstein's Theory of Gravity

Explore a nonsmooth approach to Einstein's theory of gravity in this 41-minute lecture from the Workshop on "Non-regular Spacetime Geometry" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the challenges of Einstein's smooth formulation of gravity in light of Hawking and Penrose's singularity theorems. Examine the successful theory of metric and metric-measure geometry in positive-definite signature, which allows for nonsmooth limits under dimension and curvature bounds. Investigate recent progress in developing an analogous theory for Lorentzian signature, aiming to create a nonsmooth theory of gravity. Learn about Kunzinger and Saemann's theory of Lorentzian length spaces, focusing on the time-separation function. Discover the compatibility of different notions of timelike geodesics and explore a synthetic reformulation of the null energy condition. Gain insights into the consistency and stability properties of this approach, bridging the gap between smooth and nonsmooth geometries in the context of Einstein's theory of gravity.

Robert McCann - A nonsmooth approach to Einstein‘s theory of gravity