The Geometry of the Frame Bundle over Spacetime

Details The Geometry of the Frame Bundle over Spacetime The Geometry of the Frame Bundle over Spacetime

2000-06-13

arxiv.org/abs/gr-qc/0006049v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, no figures, LaTeX 2e with AMSLaTeX 1.2 and AMSFonts, submitted to J. Math. Phys

Scientific paper

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).

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