Circular Holonomy and Clock Effects in Stationary Axisymmetric Spacetimes

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.

23 pages latex(2e) iopart style, with 1 pictex figure and 2 eps figures

References in corpus (3)

• 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
• Gravitomagnetism and Relative Observer Clock Effects

Cited by in corpus (15)

• Standard Clocks, Orbital Precession and the Cosmological Constant
• Dynamics of Extended Spinning Masses in a Gravitational Field
• Gravitational induction
• Holonomy and gravitomagnetism
• Gravitomagnetic Helicity
• Relativistic tidal effects on clock-comparison experiments
• Circular Holonomy, Clock Effects and Gravitoelectromagnetism: Still Going Around in Circles After All These Years
• Frenet-Serret formalism for null world lines
• Loop variables in the geometry of a rotating black string
• Curved accretion disks around rotating black holes without reflection symmetry
• Physical frames along circular orbits in stationary axisymmetric spacetimes
• Geometric transport along circular orbits in stationary axisymmetric spacetimes
• Holonomy Transformation in the FRW Metric
• Numerical solution of Mathisson-Papapetrou-Dixon equations for spinning test particles in a Kerr metric
• Review of the Gravitomagnetic Clock Effect