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

作者：Whale B E^*

来源：General Relativity and Gravitation, 2014, 46(1): 1624.

DOI：10.1007/s10714-013-1624-8

• Boundary
• Construction
• Chart
• Global
• Structure

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.

• 出版日期2014-1