The Sagnac effect in conformal Weyl gravity

Abstract

We investigate the Sagnac effect, representing the difference in travel time or phase shift observed for relativistic matter or light beams counter-propagating in a rotating interferometer. This is done for the Schwarzschild-like and Kerr-like vacuum solutions of conformal gravity which describe the field around a massive static and rotating object respectively, in the fourth order theory. To do this we employ the formal analogy between the Sagnac and Aharonov–Bohm effects that has been used earlier to study this effect in flat and curved spacetimes in general relativity. In particular we show that the linear term in the static metric of conformal gravity has a diminishing effect on the Sagnac time delay. Moreover using the expression for the Sagnac effect in the rotating Kerr-like spacetime, we show that the detection of the Weyl gravity contributions to the Sagnac time delay in the case of the Earth, lies beyond the capability of current experiments.