For compact binary systems with non-rotating components post-Newtonian (pN) approximation schemes have turned out to be especially successful (in explicit analytic calculations this yielded the 3.5pN-order, i.e. order (1/c^{2})^{3.5}, with c being the speed of light). Although pN-approximations assume weak gravitational fields and small velocities (v < c/3), they are usefull for the description of the low-velocity motion of compact objects (neutron stars, black holes), as in that case the strong self-gravitation of the celestial bodies is frozen in to a great extend and is therefore dynamically decoupled from its trajectory.

- The stress-energy tensor flow algebra of gravitating classicle particles with spin
- Hamiltonian 3.5pN-spin-orbit- and 4pN-spin-spin-dynamics of binary black holes
- Orbital- and spin-movements of binary black holes in higher pN-orders