  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.
