Null Distance and Convergence of Lorentzian Length Spaces
Michael Kunzinger, Roland Steinbauer
Abstract
The null distance of Sormani and Vega encodes the manifold topology as well as the causality structure of a (smooth) spacetime. We extend this concept to Lorentzian length spaces, the analog of (metric) length spaces, which generalize Lorentzian causality theory beyond the manifold level. We then study Gromov-Hausdorff convergence based on the null distance in warped product Lorentzian length spaces and prove first results on its compatibility with synthetic curvature bounds.
Topics & Concepts
MathematicsCausal structureManifold (fluid mechanics)Null (SQL)Pure mathematicsMetric spaceCausality (physics)Hausdorff spaceSpacetimeConvergence (economics)CurvatureTopology (electrical circuits)Mathematical analysisGeometryCombinatoricsPhysicsComputer scienceMechanical engineeringEconomic growthEconomicsEngineeringDatabaseQuantum mechanicsGeometric Analysis and Curvature FlowsAdvanced Differential Geometry ResearchAdvanced Operator Algebra Research