English

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

General Relativity and Quantum Cosmology 2014-02-27 v2

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.

Keywords

Cite

@article{arxiv.1401.1287,
  title  = {The chart based approach to studying the global structure of a spacetime induces a coordinate invariant boundary},
  author = {Ben Whale},
  journal= {arXiv preprint arXiv:1401.1287},
  year   = {2014}
}

Comments

46 pages, 4 images, to be published in General Relativity and Gravitation