## 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.