(ed.). Gravitational waves (IOP, 2001)(422s).

70 Mass- and current-quadrupole radiation6.5 Radiation in the Newtonian limitThe calculation so far has been within the assumptions of linearized theory. Realsources are likely to have significant self-gravity. This means, in particular,that there will be a significant component of the source energy in gravitationalpotential energy, and this must be taken into account.In fact a more realistic equation than equation (6.1) would be£ ¯h αβ =−16π(T αβ + t αβ, ) (6.47)where t αβ is the stress-energy pseudotensor of gravitational waves. This is hardto work with: equation (6.47) is an implicit equation because t αβ depends on ¯h αβ .Fortunately, the formulae that we have derived are more robust than theyseem. It turns out that the leading order radiation field from a Newtonian sourcehas the same formula as in linearized theory. By leading order we mean thedominant radiation. If there is mass-quadrupole radiation, then the mass-octupoleradiation from a Newtonian source will not be given by the formulae of thelinearized theory. On the other hand, current-quadrupole and mass-quadrupoleradiation can coexist, because they have different symmetries, so the work wehave done here is generally applicable.More details on how one calculates radiation to higher order in theNewtonian limit will be given in Blanchet’s contribution in this book. This isparticularly important for computing the radiation to be expected from coalescingbinary systems, whose orbits become highly relativistic just before coalescenceand which are, therefore, not well described by linearized theory.