Holonomy in the Schwarzschild-Droste Geometry
arXiv:gr-qc/0008070 · doi:10.1088/0264-9381/18/7/306
Abstract
Parallel transport of vectors in curved spacetimes generally results in a deficit angle between the directions of the initial and final vectors. We examine such holonomy in the Schwarzschild-Droste geometry and find a number of interesting features that are not widely known. For example, parallel transport around circular orbits results in a quantized band structure of holonomy invariance. We also examine radial holonomy and extend the analysis to spinors and to the Reissner-Nordström metric, where we find qualitatively different behavior for the extremal () case. Our calculations provide a toolbox that will hopefully be useful in the investigation of quantum parallel transport in Hilbert-fibered spacetimes.
18 Latex pages, 3 figures. Second replacement. This version as published in CQG with some misprints corrected
References in corpus (3)
Cited by in corpus (15)
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