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

Abstract

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.

27 pages, latex(2e), ws-p9-75x6-50 class, uses overcite package, 7 pictex figures, 3 eps figures; to appear in the Proceedings of the 9th ICRA Network Workshop on Fermi and Astrophysics (2001), Eds. R. Ruffini and C. Sigismondi, World Scientific, 2003. Killing tensor remarks corrected. Figure 7 slightly corrected

References in corpus (5)

• The Many Faces of Gravitoelectromagnetism
• The intrinsic derivative and centrifugal forces in general relativity: II. Applications to circular orbits in some familiar stationary axisymmetric spacetimes
• The intrinsic derivative and centrifugal forces in general relativity: I. Theoretical foundations
• On Radar Time and the Twin `Paradox'
• Circular Holonomy and Clock Effects in Stationary Axisymmetric Spacetimes

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• Gyroscope precession along unbound equatorial plane orbits around a Kerr black hole
• Black hole geodesic parallel transport and the Marck recipe for isolating cumulative precession effects
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