Spin precession in general stationary and axisymmetric spacetimes

This paper investigates the spin precession of test particles moving in the equatorial plane of general stationary and axisymmetric spacetimes using the Mathisson-Papapetrou-Dixon equations. The spin precession angles for two cases, the small-spin case and the spin-orbital plane parallel case, are derived using different approximations. For the small-spin case, the precession angle of the spin components in the equatorial plane along circular orbits is found, and perpendicular component is shown to be a constant of motion. For the spin-orbital plane parallel case, it is shown that in general the orbital and spin motions generally do not affect each other, and the spin precession angle is calculated using the post-Newtonian method to an arbitrarily high order of the orbital semi-latus rectum p. The precession angles in both cases are analyzed both qualitatively and quantitatively in the Kerr-Newman spacetime to elucidate their features. For large orbital radii, it is shown that the leading order of the precession angle series is generally proportional to the spacetime mass while the Lense-Thirring effect always appears from the subleading order. These precession results are then applied to various astronomical systems to determine their spin precession rates. For systems with observational data, our results show excellent agreement. For systems without observational data, we predict their spin precession rates at both the leading and Lense-Thirring effect orders. These predictions indicate that Jupiter's satellites exhibit exceptionally large geodetic spin precession and their Lense-Thirring effect may be detectable with current technology.