Spin-induced non-geodesic motion, gyroscopic precession, Wigner rotation and EPR correlations of massive spin 1/2 particles in a gravitational field

Understand

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.