A review of Lorentzian synthetic theory of timelike Ricci curvature bounds

被引：7
|
作者：
Cavalletti, Fabio [1 ]
Mondino, Andrea [2 ]
机构：
[1] SISSA, Math Area, Via Bonomea 265, I-34136 Trieste, TS, Italy
[2] Univ Oxford, Math Inst, Radcliffe Observ, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England
来源：
GENERAL RELATIVITY AND GRAVITATION | 2022年 / 54卷 / 11期
基金：
欧洲研究理事会;
关键词：
Ricci curvature; Optimal transport; Singularity theorem; Einstein equations; Lorentzian pre-length spaces; Lorentzian metrics of low regularity; METRIC-MEASURE-SPACES; GRAVITATIONAL COLLAPSE; DIMENSION CONDITION; BLACK-HOLES; INEQUALITY; TRANSPORT; SINGULARITIES; RECONSTRUCTION; HYPERBOLICITY; INTERPOLATION;
D O I：
10.1007/s10714-022-03004-4
中图分类号：
P1 [天文学];
学科分类号：
0704 ;
摘要：
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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页数：39
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