Post-Newtonian corrections to the motion of spinning bodies in nonrelativistic general relativity

In this paper we include spin and multipole moment effects in the formalism used to describe the motion of extended objects recently introduced in hep-th/0409156. A suitable description for spinning bodies is developed and spin-orbit, spin-spin, and quadrupole-spin Hamiltonians are found at leading order. The existence of tidal as well as self-induced finite size effects is shown, and the contribution to the Hamiltonian is calculated in the latter. It is shown that tidal deformations start formally at O(v(6)) and O(v(10)) for maximally rotating general and compact objects, respectively, whereas self-induced effects can show up at leading order. Agreement is found for the cases where the results are known.