Erratum: Post-Newtonian Gravitational Radiation from Orbiting Point Masses

Abstract

General formulae are derived which describe the gravitational radiation at large distances from a system of bodies whose sizes are small compared with their separations. The calculation is carried out through post-Newtonian order within general relativity. More explicit formulae are derived for two-body systems, and detailed results are presented for circular orbits, gravi-tational bremsstrahlung, and head-on collisions. Subject headings: gravitation-relativity-stars: binaries I. INTRODUCTION AND SUMMARY The continuing development of gravitational-wave detectors has fostered new techniques for calculating the gravitational waves emitted by astrophysical systems. These efforts have been directed toward expanding the realm of validity within general relativity of gravitational-wave formulae in order to obtain more accurate estimates of the nature and amount of gravitational radiation that experimentalists might expect to detect. (For a recent review see Thorne 1975; also Thorne and Kovács 1975.) The formalism that we shall employ is that developed by Epstein and Wagoner (1975; hereafter referred to as EW). It essentially extends the post-Newtonian analysis initiated by Chandrasekhar (1965) to gravitational radiation. We shall employ units in which G = c = 1, and adopt the other conventions and notation of EW, which should be read as background to this paper. The EW formalism yields expressions for the transverse-traceless (TT) part (§ II) of the asymptotic metric perturbation A iy TT (/,7 = 1, 2, 3) in terms of time derivatives of moments of the stress-energy distribution in the source. These moments are written as expansions in the small parameter c, where