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The Geometry of the Frame Bundle over Spacetime

Fredrik Ståhl
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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).

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Fredrik Ståhl. 2000-06-13. The Geometry of the Frame Bundle over Spacetime. https://arxiv.org/abs/gr-qc/0006049

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