2023/05/03 by Saúl Burgos, Burgos, Saúl, José Luis Flores +3 · 1 citation
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Ophthalmology and Eye Disorders
paper · pdf · doi:10.48550/arxiv.2305.02004
openalex publication_date 2023/05/03 · openalex created_date 2023/09/08 · openalex updated_date 2026/08/01
Inspired by some Lorentzian versions of the notion of metric and length space introduced by Kunzinger and Sämman, and more recently, by Müller, and Minguzzi and Sühr, we revisit the notion of Lorentzian metric space in order to later construct the c-completion of these general objects. We not only prove that this construction is feasible in great generality for these objects, including spacetimes of low regularity, but also endow the c-completion with a structure of Lorentzian metric space by itself. We also prove that the c-completion constitutes a well-suited extension of the original space, which really completes it in a precise sense and becomes sensible to certain causal properties of that space.