Relativistic effects due to gravimagnetic moment of a rotating body

We compute the exact Hamiltonian (and corresponding Dirac brackets) for a spinning particle with gravimagnetic moment κ in an arbitrary gravitational background. The case κ=0 corresponds to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations. κ=1 leads to modified MPTD equations with improved behavior in the ultrarelativistic limit. So we study the modified equations in the leading post-Newtonian approximation. The rotating body with unit gravimagnetic moment has qualitatively different behavior as compared with the MPTD body: (A) If a number of gyroscopes with various rotation axes are freely traveling together, the angles between the axes change with time. (B) For specific binary systems, gravimagnetic moment gives a contribution to the frame-dragging effect with the magnitude that turns out to be comparable with that of Schiff frame dragging.