The chart based approach to studying the global structure of a spacetime induces a coordinate invariant boundary

I demonstrate that the chart based approach to the study of the global structure of Lorentzian manifolds induces a homeomorphism of the manifold into a topological space as an open dense set. The topological boundary of this homeomorphism is a chart independent boundary of ideal points equipped with...

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Bibliographic Details
Published in:arXiv.org 2014-02
Main Author: Whale, Ben
Format: Article
Language:English
Subjects:
Manifolds (mathematics)
Spacetime
Topology
Online Access:Get full text
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Summary:I demonstrate that the chart based approach to the study of the global structure of Lorentzian manifolds induces a homeomorphism of the manifold into a topological space as an open dense set. The topological boundary of this homeomorphism is a chart independent boundary of ideal points equipped with a topological structure and a physically motivated classification. I show that this new boundary contains all other boundaries that can be presented as the topological boundary of an envelopment. Hence, in particular, it is a generalisation of Penrose's conformal boundary. I provide three detailed examples: the conformal compactification of Minkowski spacetime, Scott and Szekeres' analysis of the Curzon singularity and Beyer and Hennig's analysis of smooth Gowdy symmetric generalised Taub-NUT spacetimes.
ISSN:2331-8422
DOI:10.48550/arxiv.1401.1287