Combinatorics

Physics

Spacetime

Causal structure

Topology (electrical circuits)

Metric space

Pure mathematics

Mathematics

Economic growth

Manifold (fluid mechanics)

Engineering

Mathematical analysis

Economics

Null (SQL)

Hausdorff space

Curvature

Geometry

Convergence (economics)

Computer science

Quantum mechanics

Causality (physics)

Database

Mechanical engineering

Annales Henri Poincaré

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.

Null Distance and Convergence of Lorentzian Length Spaces