Escape of gravitational radiation from the field of massive bodies

We consider a compact source of gravitational waves of frequency ω, in or near a massive spherically symmetric distribution of matter or a black hole. Recent calculations have led to apparently contradictory results for the influence of the massive body on the propagation of the waves. We show here that the results are in fact consistent and in agreement with the ‘‘standard’’ viewpoint in which the high-frequency compact source produces the radiation as if in a flat background, and the background curvature affects the propagation of these waves.