The Geometry of the Frame Bundle over Spacetime
نویسنده
چکیده
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 Γ 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 Γ is the Levi-Cività 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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