The limit space of a Cauchy sequence of globally hyperbolic spacetimes

TL;DR

This paper constructs a unique limit space from a Cauchy sequence of globally hyperbolic spacetimes, revealing complex causal structures and defining Lorentz space dimension in line with Gromov's Riemannian approach.

Contribution

It introduces a method to construct and analyze the limit space of a Cauchy sequence of globally hyperbolic spacetimes, including its causal properties and dimension definition.

Findings

Limit space is unique up to isometry.

Limit space exhibits complex causal behavior.

A Lorentz space dimension consistent with Gromov's Riemannian definition.

Abstract

In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In the second section, I work gradually towards a construction of the limit space. I prove the limit space is unique up to isometry. I als show that, in general, the limit space has quite complicated causal behaviour. This work prepares the final paper in which I shall study in more detail properties of the limit space and the moduli space of (compact) globally hyperbolic spacetimes (cobordisms). As a fait divers, I give in this paper a suitable definition of dimension of a Lorentz space in agreement with the one given by Gromov in the Riemannian case.