The second fundamental form of a spatial slice in a torsional spacetime is a sum of the Hubble term and an extrinsic torsion term, producing a negative bias in Hubble estimates when torsion is neglected.
Holonomy in the Schwarzschild-Droste Geometry
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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-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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Intrinsic Torsion, Extrinsic Torsion, and the Hubble Parameter
The second fundamental form of a spatial slice in a torsional spacetime is a sum of the Hubble term and an extrinsic torsion term, producing a negative bias in Hubble estimates when torsion is neglected.