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

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

2005-10-10

arxiv.org/abs/gr-qc/0510047v2

Gen.Rel.Grav. 37 (2005) 1845-1855

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1007/s10714-005-0190-0

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.

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