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arxiv: 1401.1287 · v2 · pith:RYI6XKOLnew · submitted 2014-01-07 · 🌀 gr-qc

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

classification 🌀 gr-qc
keywords boundarytopologicalchartstructureanalysisapproachconformalglobal
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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.

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