Gravitational plane waves and their detection start the chapter off in parallel with electromagnetic plane waves and their detection. Geodesic deviation is reviewed and allows for a brief introduction to LIGO. The stress tensor source of radiation (and therefore, at least local, plane waves) and its conservation of energy and momentum are tied to the radiation solution of the linearized form of Einstein’s equation. A highlight is the role of gauge freedom in making gravitational plane waves physically relevant (by gauge fixing to reveal the underlying plus and cross polarizations). Power loss to gravitational radiation is discussed in the linearized limit by comparison with electric quadrupole radiation.

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