Abstract Lorentzian metric spaces and their Gromov-Hausdorff convergence

Abstract: A definition for `bounded Lorentzian metric space' is presented and discussed. This is an abstract notion of Lorentzian metric space that is sufficiently general to comprise compact causally convex subsets of globally hyperbolic (smooth) spacetimes, and causets. It is shown that a generalization of the Gromov-Hausdorff distance and convergence can be applied to these spaces. Furthermore, two additional axioms of timelike connectedness and existence of maximizers, which are stable under GH-convergence, lead to suitable notions of Lorentzian pre-length and length spaces. Similarly, sectional curvature bounds stable under GH-convergence can be introduced. A (pre)compactness theorem is also mentioned and its limitations are discussed. Talk based on joint work with Stefan Suhr (Bochum).

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( video )

---

JoMaReC - Joint Online Mathematical Relativity Colloquium

Series comments: This monthly online colloquium is meant to be accessible to and informative for mathematicians and mathematical physicists with a background in General Relativity, widely interpreted to include Lorentzian Geometry, and Geometric Analysis of various Partial Differential Equations related to General Relativity.

It is aimed to present motivation and applications of particular results and/or introduce specific subfields, while refraining from too much technicalities.

---