Geometric treatment of the gravitomagnetic clock effect

TL;DR

This paper presents a geometric framework for analyzing the gravitomagnetic clock effect applicable to any stationary axisymmetric spacetime, simplifying calculations by modeling world lines as helices on a cylindrical surface.

Contribution

It introduces a novel geometric approach to the gravitomagnetic clock effect that generalizes previous methods and applies to Kerr and weak field metrics.

Findings

Recovered known results for Kerr spacetime.

Derived formulas for time delays and synchrony defects.

Unified treatment applicable to various stationary axisymmetric metrics.

Abstract

We have developed a general geometric treatment of the GCE valid for any stationary axisymmetric metric. The method is based on the remark that the world lines of objects rotating along spacely circular trajectories are in any case, for those kind of metrics, helices drawn on the flat bidimensional surface of a cylinder. Applying the obtained formulas to the special cases of the Kerr and weak field metric for a spinning body, known results for time delays and synchrony defects are recovered.