The Sagnac Effect in curved space-times from an analogy with the Aharonov-Bohm Effect

TL;DR

This paper explores the Sagnac effect in curved space-times by drawing an analogy with the gravito-magnetic Aharonov-Bohm effect, extending previous flat space-time results to various stationary, axially symmetric geometries.

Contribution

It generalizes the gravito-magnetic Aharonov-Bohm analogy to include General Relativistic corrections in different curved space-times.

Findings

Derived corrections to the Sagnac effect in Kerr space-time

Extended the analogy to G"odel universe and Schwarzschild space-time

Demonstrated the formalism's applicability to various stationary geometries

Abstract

In the context of the natural splitting, the standard relative dynamics can be expressed in terms of gravito-electromagnetic fields, which allow to formally introduce a gravito-magnetic Aharonov-Bohm effect. We showed elsewhere that this formal analogy can be used to derive the Sagnac effect in flat space-time as a gravito-magnetic Aharonov-Bohm effect. Here, we generalize those results to study the General Relativistic corrections to the Sagnac effect in some stationary and axially symmetric geometries, such as the space-time around a weakly gravitating and rotating source, Kerr space-time, G\"{odel} universe and Schwarzschild space-time.