Degeneracy of the b-boundary in General Relativity
arXiv:gr-qc/9906021 · doi:10.1007/s002200050761
Abstract
The b-boundary construction by B. Schmidt is a general way of providing a boundary to a manifold with connection. It has been shown to have undesirable topological properties however. C. J. S. Clarke gave a result showing that for space-times, non-Hausdorffness is to be expected in general, but the argument contains some errors. We show that under somewhat different conditions on the curvature, the b-boundary will be non-Hausdorff, and illustrate the degeneracy by applying the conditions to some well known exact solutions of general relativity.
25 pages, AMS-LaTeX v1.2, AMSFonts, submitted to Commun. Math. Phys