Vorticity, Gyroscopic precession, and Spin-Curvature Force

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