Circular holonomy and clock effects in stationary axisymmetric spacetimes

Abstract

Stationary axisymmetric spacetimes containing a pair of oppositely rotating periodically intersecting circular geodesics allow us to study the 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.