On Imprisoned Curves and b-length in General Relativity
| dc.creator | Ståhl, Fredrik | |
| dc.date | 2000-06-13 | |
| dc.date.accessioned | 2026-07-25T16:59:11Z | |
| dc.description | This paper is concerned with two themes: imprisoned curves and the b-length functional. In an earlier paper by the author, it was claimed that an endless incomplete curve partially imprisoned in a compact set admits an endless null geodesic cluster curve. Unfortunately, the proof was flawed. We give an outline of the problem and remedy the situation by providing a proof by different methods. Next, we obtain some results concerning the structure of b-length neighbourhoods, which gives a clue to how the geometry of a spacetime is encoded in the pseudo-orthonormal frame bundle equipped with the b-metric. We also show that a previous result by the author, proving total degeneracy of a b-boundary fibre in some cases, does not apply to imprisoned curves. Finally, we correct some results in the literature linking the b-lengths of general curves in the frame bundle with the b-length of the corresponding horizontal curves. | |
| dc.description | 26 pages, 7 figures, LaTeX 2e with AMSLaTeX 1.2 and AMSFonts, submitted to J. Math. Phys | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0006050 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0006050 | |
| dc.identifier.uri | https://dspace.dare.co.zw/handle/123456789/44774 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | On Imprisoned Curves and b-length in General Relativity | |
| dc.type | text |