Holonomy and gravitomagnetism

We analyse parallel transport of a vector field around an equatorial orbit in the Kerr and stationary axisymmetric spacetimes that are reflection symmetric about their equatorial planes. As in the 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.