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Circular Holonomy and Clock Effects in Stationary Axisymmetric Spacetimes

By Donato Bini, Robert T. Jantzen and Bahram Mashhoon

Abstract

Stationary axisymmetric spacetimes containing a pair of oppositely-rotating periodically-intersecting circular geodesics allow the study of various so-called `clock effects' by comparing either observer or geodesic proper time periods of orbital circuits defined by the observer or the geodesic crossing points. This can be extended from a comparison of clocks to a comparison of parallel transported vectors, leading to the study of special elements of the spacetime holonomy group. The band of holonomy invariance found for a dense subset of special geodesic orbits outside a certain radius in the static case does not exist in the nonstatic case. In the Kerr spacetime the dimensionless frequencies associated with parallel transport rotations can be expressed as ratios of the proper and average coordinate periods of the circular geodesics.Comment: 23 pages latex(2e) iopart style, with 1 pictex figure and 2 eps figure

Topics: General Relativity and Quantum Cosmology
Publisher: 'IOP Publishing'
Year: 2001
DOI identifier: 10.1088/0264-9381/19/1/302
OAI identifier: oai:arXiv.org:gr-qc/0111028

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