Kerr Solution Consistent Motion of Spin Particles in the General   Relativity
  The paper presents equations determining the particle spin evolution in the post-Newtonian approximation in the problem of motion of two mass and spin possessing particles. The equations are derived with the Einstein-Infeld-Hoffmann method from the condition of metric tensor symmetry. The consideration uses the condition of coordinate harmonicity and the metric coincidence nearby the particles with expansions of the Kerr solution written in the harmonic coordinates. For gyroscopes on satellites Gravity Probe B, for example, the equations yield a deviation of the axis of revolution, which is, first, two times as small as that obtained by J.L.Anderson in paper gr-qc/0511093 and, second, the deviation is of opposite sense. From the equations it follows that the total angular momentum of the spin particle system, generally speaking, is not conserved, beginning even with the post-Newtonian approximation. The results are briefly discussed. 
Mikhail V. Gorbatenko and Taras M. Gorbatenko