# Part B: Compact Binary Systems

The problem of the motion and gravitational radiation of compact objects in post-Newtonian
approximations of general relativity is of crucial importance, for at least three reasons. First, the motion of
objects at the 1PN level (), according to the Einstein-Infeld-Hoffmann equations [69], is
routinely taken into account to describe the Solar System dynamics (see Ref. [104]). Second, the
gravitational radiation-reaction force, which appears in the equations of motion at the 2.5PN order, has
been verified by the observation of the secular acceleration of the orbital motion of the binary
pulsar [140, 141, 139]. Third, the forthcoming detection and analysis of the gravitational waves emitted by
inspiralling compact binaries will necessitate the prior knowledge of the equations of motion and radiation
up to the high 3PN relative order [48, 49, 72, 50, 135, 121, 122, 96, 59].

## 8 Hadamard Self-Field Regularization