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. Cavalletti
Primo
;
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.
Einstein equations; Lorentzian metrics of low regularity; Lorentzian pre-length spaces; Optimal transport; Ricci curvature; Singularity theorem;
Settore MAT/05 - Analisi Matematica
nov-2022
29-ott-2022
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1050234
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