The limit space of a Cauchy sequence of globally hyperbolic spacetimes

Details The limit space of a Cauchy sequence of globally hyperbolic spacetimes The limit space of a Cauchy sequence of globally hyperbolic spacetimes

2003-08-22

arxiv.org/abs/gr-qc/0308075v4

Class.Quant.Grav. 21 (2004) 851-874

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

31 pages, 5 figures, submitted to Classical and Quantum gravity, seriously improved presentation

Scientific paper

10.1088/0264-9381/21/4/008

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.

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