Upper limit on NUT charge from the observed terrestrial Sagnac effect

Abstract

The \textit{exact} Sagnac delay in the Kerr-Taub-NUT (Newman-Unti-Tamburino) spacetime is derived in the equatorial plane for non-geodesic as well as geodesic circular orbits. The resulting formula, being exact, can be directly applied to motion in the vicinity of any spinning object including black holes but here we are considering only the terrestrial case since observational data are available. The formula reveals that, in the limit of spin $a\rightarrow 0$, the delay does not vanish. This fact is similar to the non-vanishing of Lense-Thirring precession under $a\rightarrow 0$ even though the two effects originate from different premises. Assuming\ a reasonable input that the Kerr-Taub-NUT\ corrections are subsumed in the average residual uncertainty in the measured Sagnac delay, we compute upper limits on the NUT charge $n$. It is found that the upper limits on $n$ are far larger than the Earth's gravitational mass, which has not been detected in observations, implying that the Sagnac effect cannot constrain $n$ to smaller values near zero. We find a curious difference between the delays for non-geodesic and geodesic clock orbits and point out its implication for the well known "twin paradox" of special relativity.