The Geometry of the Frame Bundle over Spacetime
General Relativity and Quantum Cosmology
2007-05-23 v1
Abstract
One of the known mathematical descriptions of singularities in General Relativity is the b-boundary, which is a way of attaching endpoints to inextendible endless curves in a spacetime. The b-boundary of a manifold M with connection is constructed by forming the Cauchy completion of the frame bundle LM equipped with a certain Riemannian metric, the b-metric G. We study the geometry of (LM,G) as a Riemannian manifold in the case when the connection is the Levi-Civita connection of a Lorentzian metric g on M. In particular, we give expressions for the curvature and discuss the isometries and the geodesics of (LM,G) in relation to the geometry of (M,g).
Cite
@article{arxiv.gr-qc/0006049,
title = {The Geometry of the Frame Bundle over Spacetime},
author = {Fredrik Ståhl},
journal= {arXiv preprint arXiv:gr-qc/0006049},
year = {2007}
}
Comments
14 pages, no figures, LaTeX 2e with AMSLaTeX 1.2 and AMSFonts, submitted to J. Math. Phys