Academic Journal
The chart based approach to studying the global structure of a spacetime induces a coordinate invariant boundary.
| Title: | The chart based approach to studying the global structure of a spacetime induces a coordinate invariant boundary. |
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| Authors: | Whale, B. |
| Source: | General Relativity & Gravitation; Jan2014, Vol. 46 Issue 1, p1-43, 43p |
| 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. [ABSTRACT FROM AUTHOR] |
| Subject Terms: | SPACETIME, INVARIANTS (Mathematics), LORENTZIAN function, MANIFOLDS (Mathematics), HOMEOMORPHISMS, TOPOLOGICAL spaces, MINKOWSKI space |
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| ISSN: | 00017701 |
| DOI: | 10.1007/s10714-013-1624-8 |
| Database: | Complementary Index |