# A Lorentzian Gromov–Hausdorff notion of distance

@article{Noldus2003ALG, title={A Lorentzian Gromov–Hausdorff notion of distance}, author={Johan Noldus}, journal={Classical and Quantum Gravity}, year={2003}, volume={21}, pages={839-850} }

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 two papers. The importance of the work is in fields such as cosmology, quantum gravity and?for the mathematicians?global Lorentzian geometry.

## 25 Citations

### The moduli space of isometry classes of globally hyperbolic spacetimes

- Mathematics
- 2004

This paper is part of a research programme on the structure of the moduli space of Lorentzian geometries, a Lorentzian analogue of Gromov–Hausdorff theory based on the use of the Lorentz distance as…

### The moduli space of isometry classes of globally hyperbolic spacetimes

- Mathematics
- 2004

This paper is part of a research programme on the structure of the moduli space of Lorentzian geometries, a Lorentzian analogue of Gromov–Hausdorff theory based on the use of the Lorentz distance as…

### On generalizations of the Lorentzian distance function Contents

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- 2018

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- 2003

In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In section 2, I work gradually towards a construction of the limit space. I prove that the…

### Lorentzian metric spaces and their Gromov-Hausdorff convergence

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- 2022

We present an abstract approach to Lorentzian Gromov-Hausdorff distance and convergence. We begin by defining a notion of (abstract) bounded Lorentzian-metric space which is sufficiently general to…

### Properties of the Null Distance and Spacetime Convergence

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- 2021

The null distance for Lorentzian manifolds was recently introduced by Sormani and Vega. Under mild assumptions on the time function of the spacetime, the null distance gives rise to an intrinsic,…

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- 2012

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### ON THE GEOMETRY OF LORENTZ SPACES AS A LIMIT SPACE

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Abstract. In this paper, we prove that there is no branch point in theLorentz space (M,d) which is the limit space of a sequence {(M α ,d α )}ofcompact globally hyperbolic interpolating spacetimes…

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### Minkowski space is locally the Noldus limit of Poisson process causets

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A Poisson process P λ on R d with causal structure inherited from the the usual Minkowski metric on R d has a normalised discrete causal distance D λ ( x , y ) given by the height of the longest…

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