On the assumptions made in treating the gravitational wave problem by the high-frequency approximation

The assumptions that enter into the formulation of the gravitational wave problem in the limit of high frequency are discussed. It is shown that depending on the relation between the amplitude parameter and the frequency parameter the concept of back-reaction can have different physical interpretations. We also show that as a direct consequence of these assumptions high-frequency gravitational waves do not disperse in a vacuum. Finally, we make some conjectures about a coordinate-free characterization of high frequency for some cases and also about the use of the invariants of the Weyl tensor for the problem of finding a background space-time given a vacuum space-time containing high-frequency gravitational radiation.