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arXiv · gr-qc/0008070

Holonomy in the Schwarzschild-Droste Geometry

Tony Rothman·George F. R. Ellis·Jeff Murugan
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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 ($Q = M$) 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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Tony Rothman, George F. R. Ellis, Jeff Murugan. 2001-05-15. Holonomy in the Schwarzschild-Droste Geometry. https://doi.org/10.1088/0264-9381%2F18%2F7%2F306

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