The gravitational field of a black hole differs significantly from the point-mass field that is normally used in N-Body simulations. The additional terms needed are called Post-Newtonian ones and abbreviated as PN-terms. They depend in addition of coordinates also on velocities. Thus the methods discussed in Section~\ref{v-dependence} must be used in numerical integration. An other problem is that the orbital elements of two-body motions cannot any more be evaluatedin the same way as in the Newtonian point-mass dynamics. Finally one must remember that black holes rotate and form a so called Kerr-hole that produce a fielddiffering from the non-rotating one and the rotation, the black hole spin, changes due to interactions withother bodies. These complexities is discussed and formulae given in this short chapter