In the preceding three chapters we stayed safely in the near zone and ignored all radiative aspects of the motion of bodies subjected to a mutual gravitational interaction. In this chapter we move to the wave zone and determine the gravitational waves produced by the moving bodies. To achieve this goal we must return to the post-Minkowskian approximation developed in Chapters 6 and 7, because the post-Newtonian techniques of Chapter 8 are necessarily restricted to the near zone.

We begin in Sec. 11.1 by reviewing the notion of far-away wave zone, in which the gravitational-wave field can be extracted from the (larger set of) gravitational potentials hαβ; we explain how to perform this extraction and obtain the gravitational-wave polarizations h+ and h×. In Sec. 11.2 we derive the famous quadrupole formula, the leading term in an expansion of the gravitational-wave field in powers of νc/c (with νc denoting a characteristic velocity of the moving bodies); we flesh out this discussion by examining a number of applications of the formula. Section 11.3 is a very long excursion into a computation of the gravitational-wave field beyond the quadrupole formula, in which we add corrections of fractional order (νc/c), (νc/c)2, and (νc/c)3 to the leading-order expression.