Circular Holonomy, Clock Effects and Gravitoelectromagnetism: Still Going Around in Circles After All These Years

Details Circular Holonomy, Clock Effects and Gravitoelectromagnetism: Still Going Around in Circles After All These Years Circular Holonomy, Clock Effects and Gravitoelectromagnetism: Still Going Around in Circles After All These Years

2002-02-24

arxiv.org/abs/gr-qc/0202085v2

Nuovo Cim.B117:983-1008,2003

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, latex(2e), ws-p9-75x6-50 class, uses overcite package, 7 pictex figures, 3 eps figures; to appear in the Proceedings

Scientific paper

The historical origins of Fermi-Walker transport and Fermi coordinates and the construction of Fermi-Walker transported frames in black hole spacetimes are reviewed. For geodesics this transport reduces to parallel transport and these frames can be explicitly constructed using a Killing-Yano tensor as shown by Marck. For accelerated or geodesic circular orbits in such spacetimes, both parallel and Fermi-Walker transported frames can be given, and allow one to study circular holonomy and related clock and spin transport effects. In particular the total angle of rotation that a spin vector undergoes around a closed loop can be expressed in a factored form, where each factor is due to a different relativistic effect, in contrast with the usual sum of terms decomposition. Finally the Thomas precession frequency is shown to be a special case of the simple relationship between the parallel transport and Fermi-Walker transport frequencies for stationary circular orbits.

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