Holonomy and gravitomagnetism

TL;DR

This paper investigates how parallel transport around equatorial orbits in rotating black hole spacetimes reveals a band structure of holonomy invariance, highlighting a gravitomagnetic clock effect due to rotation.

Contribution

It extends previous holonomy analyses to Kerr spacetimes, demonstrating a rotation-induced shift in the vector's timelike component linked to gravitomagnetism.

Findings

Holonomy invariance exhibits a band structure in Kerr spacetime.

Rotation causes a shift in the timelike component of transported vectors.

The shift is related to the gravitomagnetic clock effect.

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.