Holonomy in the Schwarzschild-Droste Geometry

Details Holonomy in the Schwarzschild-Droste Geometry Holonomy in the Schwarzschild-Droste Geometry

2000-08-29

arxiv.org/abs/gr-qc/0008070v4

Class.Quant.Grav. 18 (2001) 1217-1234

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 Latex pages, 3 figures. Second replacement. This version as published in CQG with some misprints corrected

Scientific paper

10.1088/0264-9381/18/7/306

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-Nordstr\"om metric, where we find qualitatively different behavior 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-fibered spacetimes.

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