Brans-Dicke corrections to the gravitational Sagnac effect

TL;DR

This paper derives the exact influence of the Brans-Dicke scalar field on the gravitational Sagnac effect, confirming known weak-field results and exploring implications for Earth's orbit and gyroscopic precession.

Contribution

It provides the first exact formulation of Brans-Dicke scalar field effects on the Sagnac delay in both Jordan and Einstein frames, including new correction estimates.

Findings

Agreement with known PPN factors in weak field limit

First-order fringe shift correction of ~0.283 for Earth orbits

Scalar field effects on gyroscopic precession analyzed

Abstract

The {\it exact} formulation for the effect of the Brans-Dicke scalar field on the gravitational corrections to the Sagnac delay in the Jordan and Einstein frames is presented for the first time. The results completely agree with the known PPN factors in the weak field region. The calculations also reveal how the Brans-Dicke coupling parameter (appears in various correction terms for different types of source/observer orbits. A first order correction of roughly 2.83 x 10^{-1} fringe shift for visible light is introduced by the gravity-scalar field combination for Earth bound equatorial orbits. It is also demonstrated that the final predictions in the two frames do not differ. The effect of the scalar field on the geodetic and Lense-Thirring precession of a spherical gyroscope in circular polar orbit around the Earth is also computed with an eye towards the Stanford Gravity Probe-B experiment currently in progress. The feasibility of optical and matter-wave interferometric measurements is discussed briefly.