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arXiv · 1401.1287

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

Ben Whale
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Abstract

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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Ben Whale. 2014-01-07. The chart based approach to studying the global structure of a spacetime induces a coordinate invariant boundary. https://doi.org/10.1007/s10714-013-1624-8

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