Geodesic precession in the \((\Omega, A_{ab})\)-field theory (Q1898072)

Suppose that a (small) torque-free gyroscope with spin \(S\) moves along a geodesic. Thus \(S\) is parallely transported. The agreement between the parallel transport and the gyroscope transport only holds along geodesic. It is known that in the curved spacetime, parallel transport has drastic effects on the direction of a vector, and we therefore expect similar effects on a gyroscope. Here, in the framework of Straumann's derivation [\textit{N. Straumann}, General relativity and relativistic astrophysics, Springer-Verlag (1986)], we present the geodesic precession in the \((\Omega, A_{ab})\)-field proposed by \textit{X. Yu} [Theory of gravitational radiation of the \((\Omega, A_{ab})\)-field, Astrophys. Space Sci. 202, No. 2, 237-246 (1993; Zbl 0784.53067)].