  We investigate in a covariant manner the spin-induced non-geodesic motion of
massive spin 1/2 particles in an arbitrary gravitational field for trajectories
that are initially geodesic when spin is ignored. Using the WKB approximation
for the wave function in curved spacetime, we compute the O(hbar) correction to
the Wigner rotation of the spin 1/2 particle, whose O(1) contribution is zero
on timelike geodesics. We develop conditions for the motion of observers in
which the Wigner rotation is null. For the spherically symmetric Schwarzschild
metric, we consider specific examples of particle motion in the equatorial
plane for (i) circular orbits and (ii) radially infalling trajectories. For the
former case we consider the entanglement for a perfectly anti-correlated EPR
entangled pair of spins as the separate qubits traverse the circular orbit in
same direction.
