Post-Newtonian Expansion of Gravitational Radiation

The post-Newtonian expansion appears to be a relevant tool for predicting thegravitational waveforms generated by some astrophysical systems such asbinaries. In particular, inspiralling compact binaries are well-modelled by asystem of two point-particles moving on a quasi-circular orbit whose decay byemission of gravitational radiation is described by a post-Newtonian expansion.In this paper we summarize the basics of the computation by means of a seriesof multipole moments of the exterior field generated by an isolated source inthe post-Newtonian approximation. This computation relies on an ansatz ofmatching the exterior multipolar field to the inner field of a slowly-movingsource. The formalism can be applied to point-particles at the price of afurther ansatz, that the infinite self-field of point-particles can beregularized in a certain way. As it turns out, the concept of point-particlerequires a precise definition in high post-Newtonian approximations of generalrelativity.Comment: In Black Holes and Gravitational Waves, Proceedings of the 9th Yukawa International Seminar, T. Nakamura and H. Kodama (eds.), Prog. Theor. Phys. Suppl. No. 136, 146 (1999