An optimal transport formulation of the Einstein equations - Second part
Quentin Dubroff - Rutgers
Location: Hill 423
Date & time: Wednesday, 18 September 2019 at 11:00AM - 12:30PM
Abstract: Inspired by recent developments in the Riemannian setting, Andrea Mondino and Stefan Suhr have established an optimal transport formulation of the Einstein equations in space-times of dimension at least three, allowing one to extend the notion of a solution to spaces of low regularity. They show the equivalence of Ricci curvature lower and upper bounds with (resp.) convexity and concavity conditions on the information-theoretic entropy along time-like displacements of a probability measure. I will present a portion of their work, providing the necessary background from optimal transport and finishing by showing the equivalence of the strong energy condition of Hawking and Penrose with the displacement convexity of the information-theoretic entropy.