A review of Lorentzian synthetic theory of timelike Ricci curvature bounds

Abstract

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.

arXiv commentFinal version, published in "General Relativity and Gravitation", special issue in honour of Roger Penrose. arXiv admin note: text overlap with arXiv:2004.08934

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• Gravity from thermodynamics: optimal transport and negative effective dimensions
• How Much NEC Breaking Can the Universe Endure?
• A lower semicontinuous time separation function for $C^0$ spacetimes
• Causal bubbles in globally hyperbolic spacetimes