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1 Introduction

The theory of gravitational radiation from isolated sources, in the context of general relativity, is a fascinating science that can be explored by means of what was referred to in the French XVIIIth century as l’analyse sublime: the analytical (i.e. mathematical) method, and more specifically the resolution of partial differential equations. Indeed, the field equations of general relativity, when use is made of the harmonic-coordinate conditions, take the form of a quasi-linear hyperbolic differential system of equations, involving the famous wave operator or d’Alembertian (denoted []), invented by d’Alembert in his Traité de dynamique of 1743.

Nowadays, the importance of the field lies in the exciting possibility of comparing the theory with contemporary astrophysical observations, made by a new generation of detectors - large-scale optical interferometers LIGO, VIRGO, GEO and TAMA - that should routinely observe the gravitational waves produced by massive and rapidly evolving systems such as inspiralling compact binaries. To prepare these experiments, the required theoretical work consists of carrying out a sufficiently general solution of the Einstein field equations, valid for a large class of matter systems, and describing the physical processes of the emission and propagation of the waves from the source to the distant detector, as well as their back-reaction onto the source.


 1.1 Gravitational-wave generation formalisms
 1.2 Problem posed by compact binary systems
 1.3 Post-Newtonian equations of motion and radiation

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