A Lorentzian Gromov-Hausdoff notion of distance

2003/08/31 by Johan Noldus · 6 citations
Mathematics · Medicine · Physics and Astronomy · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #gr-qc #math.MG

paper · pdf · doi:10.1088/0264-9381/21/4/007

published as Class.Quant.Grav. 21 (2004) 839-850 · 20 pages, 0 figures, submitted to Classical and quantum gravity, seriously improved presentation

arxiv created 2003/11/18 · openalex publication_date 2004/01/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a metric space. Further properties of this metric space are studied in the next papers. The importance of the work can be situated in fields such as cosmology, quantum gravity and - for the mathematicians - global Lorentzian geometry.

Citations

• A new topology on the space of Lorentzian metrics on a fixed manifold
• The origin of Lorentzian geometry

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• Foundations of a theory of quantum gravity
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• The causal set approach to quantum gravity
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• Causal sets [wikipedia]