The Sagnac effect in the Earth-Fixed rotating observer’s frame: A comparative study

Abstract

We use Einstein synchronization formalism to investigate and compare the general relativistic corrections of the Sagnac effect for an Earth-Fixed rotating observer in flat, Newtonian, Schwarzschild, and weak-Kerr backgrounds. This comparison shows that the correction due to the Earth’s angular momentum, which is only achieved in the weak-Kerr background, is equal in order of magnitude to the correction due to the Earth’s mass and larger than the correction due to the angular velocity of the rotating frame. The phase shift resulting from this time correction is measurable and therefore its consideration is of experimental importance.