Calculus of Variations and Geometric Measure Theory

A. Mondino - S. Suhr

An optimal transport formulation of the Einstein equations of general relativity

created by mondino on 01 Nov 2018
modified on 05 Jul 2021


Accepted Paper

Inserted: 1 nov 2018
Last Updated: 5 jul 2021

Journal: Journal of the European Math. Society (JEMS)
Pages: 60
Year: 2018


The goal of the paper is to give 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 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.