Vorticity, gyroscopic precession, and spin-curvature force

In investigating the relationship between vorticity and gyroscopic precession, we calculate the vorticity vector in Godel, Kerr, Lewis, Schwarzschild, and Minkowski metrics and find that the vorticity vector of the specific observers is the angular velocity of the gyroscopic precession. Furthermore, when space-time torsion is included, the vorticity and spin-curvature force change sign. This result is very similar to the behavior of the positive and negative helicities of quantum spin in the Stern-Gerlach force. It implies that the inclusion of torsion will lead to an analogous property of quantum spin even in classical treatment.