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

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.

14 pages, 1 EPS figure, LaTeX, accepted for publication in General Relativity and Gravitation

References in corpus (2)

• A direct kinematical derivation of the relativistic Sagnac effect for light or matter beams
• Sagnac Effect of Goedel's Universe

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