A new topology on the space of Lorentzian metrics on a fixed manifold

@article{Noldus2002ANT,
  title={A new topology on the space of Lorentzian metrics on a fixed manifold},
  author={Johan Noldus},
  journal={Classical and Quantum Gravity},
  year={2002},
  volume={19},
  pages={6075-6107}
}
  • Johan Noldus
  • Published 7 December 2002
  • Mathematics
  • Classical and Quantum Gravity
We give a covariant definition of closeness between (time-oriented) Lorentzian metrics on a manifold M, using a family of functions which measure the difference in volume form on one hand and, on the other, the difference in causal structure relative to a volume scale. These functions will distinguish two geometric properties of the Alexandrov sets A(p, q), (p, q) relative to two spacetime points q and p and metrics g and . It will be shown that this family generates uniformities and… 

Figures from this paper

The moduli space of isometry classes of globally hyperbolic spacetimes

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

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

A Lorentzian Lipschitz, Gromov-Hausdoff notion of distance

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

A Lorentzian Gromov–Hausdorff notion of distance

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

A Lorentzian Gromov–Hausdorff notion of distance

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

Compact Lorentzian holonomy

Similarity, Topology, and Physical Significance in Relativity Theory

Stephen Hawking, among others, has proposed that the topological stability of a property of space-time is a necessary condition for it to be physically significant. What counts as stable, however,

0 30 80 74 v 3 1 8 N ov 2 00 3 A Lorentzian Gromov-Hausdorff notion of distance

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

The causal set approach to quantum gravity

  • S. Surya
  • Physics
    Living Reviews in Relativity
  • 2019
The causal set theory (CST) approach to quantum gravity postulates that at the most fundamental level, spacetime is discrete, with the spacetime continuum replaced by locally finite posets or “causal

Stability and Genericity Aspects of Properties of Space-times in General Relativity

In this article, we review and discuss different aspects of stability and genericity of some properties of space-times which occur in various contexts in the General Theory of Relativity. We also

References

SHOWING 1-10 OF 22 REFERENCES

Statistical Lorentzian geometry and the closeness of Lorentzian manifolds

I introduce a family of closeness functions between causal Lorentzian geometries of finite volume and arbitrary underlying topology. When points are randomly scattered in a Lorentzian manifold, with

Causal continuity in degenerate spacetimes

A change of spatial topology in a causal, compact spacetime cannot occur when the metric is globally Lorentzian. On any cobordism manifold, however, one can construct from a Morse function f and an

A new topology for curved space–time which incorporates the causal, differential, and conformal structures

A new topology is proposed for strongly causal space–times. Unlike the standard manifold topology (which merely characterizes continuity properties), the new topology determines the causal,

Riemannian geometry and geometric analysis

* Established textbook * Continues to lead its readers to some of the hottest topics of contemporary mathematical research This established reference work continues to lead its readers to some of

The Large Scale Structure of Space-Time

The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions.

The Convenient Setting of Global Analysis

Introduction Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly realcompact spaces Extensions and liftings of mappings Infinite dimensional

Causal measurability in chronological spaces

We show that the causal structure determines a volume measurability up to sets of zero measure. In space-time manifolds this causal measurability, apart from sets of zero measure, agrees with the a

Linear Spaces And Differentiation Theory

Preface Foundational Material Convenient Vector Spaces Multilinear Maps and Categorical Properties Calculus in Convenient Vector Spaces Differentiable Maps and Categorical Properties The Mackey