Holonomy and gravitomagnetism

Abstract

We analyze parallel transport of a vector field around an equatorial orbit in Kerr and stationary axisymmetric spacetimes that are reflection symmetric about their equatorial planes. As in Schwarzschild spacetime, there is a band structure of holonomy invariance. The new feature introduced by rotation is a shift in the timelike component of the vector, which is the holonomic manifestation of the gravitomagnetic clock effect.

6 pages Latex (IOP style); new results covering stationary axisymmetric spacetimes; version accepted for Class. Quant. Grav

References in corpus (2)

• Gravitomagnetism and Relative Observer Clock Effects
• Circular Holonomy and Clock Effects in Stationary Axisymmetric Spacetimes

Cited by in corpus (10)

• Standard Clocks, Orbital Precession and the Cosmological Constant
• Gravitomagnetism in the Kerr-Newman-Taub-NUT spacetime
• Gravimagnetism, Causality, and Aberration of Gravity in the Gravitational Light-Ray Deflection Experiments
• Circular holonomy in the Taub-NUT spacetime
• Global aspects of gravitomagnetism
• Gravitomagnetism in the Lewis cylindrical metrics
• Physical frames along circular orbits in stationary axisymmetric spacetimes
• Geometric transport along circular orbits in stationary axisymmetric spacetimes
• Direct Detection of Universal Expansion by Holonomy in the McVittie Spacetime
• Review of the Gravitomagnetic Clock Effect