The goal 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 and 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.
A review of Lorentzian synthetic theory of timelike Ricci curvature bounds / F. Cavalletti, A. Mondino. - In: GENERAL RELATIVITY AND GRAVITATION. - ISSN 0001-7701. - 54:11(2022 Nov), pp. 137.1-137.39. [10.1007/s10714-022-03004-4]
A review of Lorentzian synthetic theory of timelike Ricci curvature bounds
F. CavallettiPrimo
;
2022
Abstract
The goal 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 and 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.
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