PIRSA:23100077

Video URL

https://pirsa.org/23100077

A Nonsmooth Approach to Einstein's Theory of Gravity

McCann, R. (2023). A Nonsmooth Approach to Einstein's Theory of Gravity. Perimeter Institute for Theoretical Physics. https://pirsa.org/23100077

McCann, Robert. A Nonsmooth Approach to Einstein's Theory of Gravity. Perimeter Institute for Theoretical Physics, Oct. 05, 2023, https://pirsa.org/23100077 

          @misc{ scivideos_PIRSA:23100077,
            doi = {10.48660/23100077},
            url = {https://pirsa.org/23100077},
            author = {McCann, Robert},
            keywords = {Strong Gravity},
            language = {en},
            title = {A Nonsmooth Approach to Einstein{\textquoteright}s Theory of Gravity},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2023},
            month = {oct},
            note = {PIRSA:23100077 see, \url{https://scivideos.org/pirsa/23100077}}
          }

Robert McCann University of Toronto

Talk numberPIRSA:23100077
DOI10.48660/23100077
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

While Einstein's theory of gravity is formulated in a smooth setting, the singularity theorems of Hawking and Penrose describe many physical situations in which this smoothness must eventually breakdown. In positive-definite signature, there is a highly successful theory of metric and metric-measure geometry which includes Riemannian manifolds as a special case, but permits the extraction of nonsmooth limits under curvature and dimension bounds analogous to the energy conditions in relativity: here sectional curvature is reformulated through triangle comparison, while Ricci curvature is reformulated using entropic convexity along geodesics of probability measures.This lecture explores recent progress in the development of an analogous theory in Lorentzian signature, whose ultimate goal is to provide a nonsmooth theory of gravity. We highlight how the null energy condition of Penrose admits a nonsmooth formulation as a variable lower bound on timelike Ricci curvature. We discuss an example showing the null energy condition does not survive the same sort of limits that uniform bounds on the timelike Ricci curvature respect. 

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Zoom link: https://pitp.zoom.us/j/92777399316?pwd=QmNaM1J0elgyRGdmaGxCTTQxT2Y4QT09