A Lorentzian Gromov-Hausdoff notion of distance

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.

20 pages, 0 figures, submitted to Classical and quantum gravity, seriously improved presentation

References in corpus (4)

• Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)
• The moduli space of isometry classes of globally hyperbolic spacetimes
• The limit space of a Cauchy sequence of globally hyperbolic spacetimes
• A new topology on the space of Lorentzian metrics on a fixed manifold

Cited by in corpus (13)

• The causal set approach to quantum gravity
• Evidence for an entropy bound from fundamentally discrete gravity
• Emergence of spatial structure from causal sets
• The moduli space of isometry classes of globally hyperbolic spacetimes
• Properties of the Null Distance and Spacetime Convergence
• The limit space of a Cauchy sequence of globally hyperbolic spacetimes
• Lorentzian Manifolds and Causal Sets as Partially Ordered Measure Spaces
• Foundations of a theory of quantum gravity
• A causal perspective on random geometry
• How Riemannian Manifolds Converge: A Survey
• Algorithmic Causal Sets and the Wolfram Model
• Results on Lorentzian metric spaces
• Minkowski space is locally the Noldus limit of a Poisson process causet