On the space of compact diamonds of Lorentzian length spaces

2023/02/23 by Waldemar Barrera, Barrera, Waldemar, Luis Montes de +3 · 1 citation
Mathematics · 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 #Geometric and Algebraic Topology #Mathematical Physics (math-ph) #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2302.11819

openalex publication_date 2023/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we introduce the taxicab and uniform products for Lorentzian pre-length spaces. We further use these concepts to endow the space D(R×_T X) of causal diamonds with a Lorentzian length space structure, closely relating its causal properties with its geometry as a metric space furnished with its associated Hausdorff distance. Among the general results, we show that this space is geodesic and globally hyperbolic for complete X.

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• The causal structure of the c-completion of warped spacetimes

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