A note on the Sagnac effect in general relativity as a Finslerian effect
Erasmo Caponio, Antonio Masiello
TL;DR
This paper reviews how the Sagnac effect's geometry in general relativity can be understood through Finsler geometry, highlighting asymmetries in spacetime and their impact on null and timelike geodesics.
Contribution
It introduces a Finslerian perspective to analyze the Sagnac effect, emphasizing the role of metric asymmetry in stationary spacetimes and extending the understanding to timelike geodesics.
Findings
Finsler geometry captures the asymmetry in the Sagnac effect.
Asymmetry in the Finsler metric relates to null geodesics.
Similar asymmetry affects timelike geodesics.
Abstract
The geometry of the Sagnac effect in a stationary region of a spacetime is reviewed with the aim of emphasizing the role of asymmetry of a Finsler metric defined on a spacelike hypersurface associated to a stationary splitting and related to future-pointing null geodesics of the spacetime. We show also that an analogous asymmetry comes into play in the Sagnac effect for timelike geodesics.
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