An optimal transport formulation of the Einstein equations of general relativity

Abstract: In the seminar I will present a recent work joint with S. Suhr (Bochum) giving an optimal transport formulation of the full Einstein equations of general relativity, linking the (Ricci) curvature of a space-time with the cosmological constant and the energy-momentum tensor. Such an optimal transport formulation is in terms of convexity/concavity properties of the Shannon-Bolzmann entropy along curves of probability measures extremizing suitable optimal transport costs. The result, together with independent work by McCann on lower bounds for Lorentzian Ricci Curvature, gives a new connection between general relativity and optimal transport; moreover it gives a mathematical reinforcement of the strong link between general relativity and thermodynamics/information theory that emerged in the physics literature of the last years.

algebraic topologydifferential geometrygeometric topologymetric geometry

Audience: researchers in the topic

Comments: The talk will be via Zoom at: us02web.zoom.us/j/81133134160 passcode 507121

University of Toronto Geometry & Topology seminar