Are there gravitational waves?

The existence of gravitational waves was disputed for a long time, but in recent years their existence has been generally accepted. As often in the history of a science, the cause of the variance of opinions is to be sought in a mixture of ignorance and inexact definitions. Probably in the theory of gravitation, too, the dispute will only be completely settled when a solution, for example, of the two-body problem, has been found, from which one can see in what sense such a double-star system in a Friedmann universe emits waves and in what sense it does not, and when the existence of such waves has been experimentally demonstrated.

Waves in the most general sense are time-dependent solutions of the Einstein equations; of course such solutions exist. But this definition of waves is, as we can see from experience with the Maxwell theory, rather too broad, for a field which changes only as a result of the relative motion of the source and the observer (motion past a static field) would not be called a wave. Most additional demands which a gravitational wave should satisfy lead, however, to the characterization ‘radiation or transport of energy’, and this is where the difficulties begin, as explained in the previous chapter, starting with the definition of energy.

In order to make the situation relatively simple, in spite of the non-linearity of the field equations, one can restrict attention to those solutions which possess a far-field zone in the sense of Section 28.1.