2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103311In 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 GravitationGeneral Relativity and Quantum Cosmologytext