Calculus of Variations and Geometric Measure Theory

F. Cavalletti - A. Mondino

A review of Lorentzian synthetic theory of timelike Ricci curvature bounds

created by cavallett on 28 Apr 2022
modified by mondino on 29 Oct 2022


Published Paper

Inserted: 28 apr 2022
Last Updated: 29 oct 2022

Journal: General Relativity and Gravitation
Year: 2022
Doi: 10.1007/s10714-022-03004-4


The scope of this survey is to give a self-contained introduction to synthetic timelike Ricci curvature bounds for (possibly non-smooth) Lorentzian spaces via optimal transport & entropy tools, including a synthetic version of Hawking’s singularity theorem and a synthetic characterisation of Einstein’s vacuum equations. We will also discuss some motivations arising from the smooth world and some possible directions for future research.