A review of Lorentzian synthetic theory of timelike Ricci curvature bounds
Fabio Cavalletti, Andrea Mondino
Abstract
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.
Topics & Concepts
Ricci curvaturePhysicsEinsteinCurvatureDifferential geometrySingularityHawkingMathematical physicsScalar curvatureTheoretical physicsEntropy (arrow of time)Pure mathematicsMathematical analysisMathematicsGeometryQuantum mechanicsGeometric Analysis and Curvature FlowsCosmology and Gravitation TheoriesAdvanced Differential Geometry Research