Equations of motion of rotating bodies in general relativity in the post-Newtonian approximation

Equations of the translational and rotational motion of two bodies possessing intrinsic angular momentum are obtained by the Einstein–Infeld–Hoffmann method in the post-Newtonian approximation. The results agree with the Kerr metric expressed in a harmonic system of coordinates with symmetry of the spatial components of the metric with respect to its indices and with a conservation law for the total angular momentum that is the sum of the orbital and spin angular momenta, and they give the correct passage to the limit to the equation of motion of a test particle with spin.