other · CERN Bulletin · 2000

The Geometry of the Frame Bundle over Spacetime

Staahl, F

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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).

Cite this paper

APA 7

Staahl, F. (2000). The Geometry of the Frame Bundle over Spacetime. CERN Bulletin.

MLA 9

Staahl, F. “The Geometry of the Frame Bundle over Spacetime.” CERN Bulletin, 2000.

Chicago

Staahl, F. 2000. “The Geometry of the Frame Bundle over Spacetime.” CERN Bulletin.

Harvard

Staahl, F. (2000) ‘The Geometry of the Frame Bundle over Spacetime’, CERN Bulletin.

BibTeX

@misc{staahl2000geometry,
  title = {{The Geometry of the Frame Bundle over Spacetime}},
  author = {Staahl, F},
  journal = {CERN Bulletin},
  year = {2000}
}

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