2000/08/31 by Tony Rothman, George F. R. Ellis, George F R Ellis +1 · 1 citation
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Geometric Analysis and Curvature Flows #Pulsars and Gravitational Waves Research #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/18/7/306
published as Class.Quant.Grav. 18 (2001) 1217-1234 · 18 Latex pages, 3 figures. Second replacement. This version as published in CQG with some misprints corrected
openalex publication_date 2001/03/14 · arxiv created 2001/05/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 a 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 behaviour for the extremal ( Q = M ) case. Our calculations provide a toolbox that will hopefully be useful in the investigation of quantum parallel transport in Hilbert-fibred spacetimes.