Gravitational Radiation in the Limit of High Frequency. I. The Linear Approximation and Geometrical Optics

Gravitational optics: Self-phase modulation and harmonic cascades

“…For a gravitational wave produced by any reasonable astrophysical event, our best expectations [14] give a ∼ 10 −21 , as the wave arrives on Earth. But, along its path from the radiation source to the Earth, its amplitude will remain significantly higher over large distances.…”

“…We are not interested in the wave generation phenomena, for which there exists a standard powerful formalism [14] valid even in strongly curved regions, nor in the propagation of gravitational waves in strongly curved regions. Here we want to focus on regions far from the sources, where the background is approximately flat.…”

Some High-Frequency Gravitational Waves Related to Exact Radiative Spacetimes

“…Isaacson's systematic study [1] stimulated further works in which his treatment was developed and also re-formulated in various formalisms. Choquet-Bruhat [7,8] analyzed high-frequency gravitational radiation using a generalized WKB "two-timing" method.…”

“…These general methods have been, of course, applied to study explicit particular examples of high-frequency gravitational waves, see e.g. [1,8,9,15,16].…”

“…In classic work [1] Isaacson presented a perturbation method which enables one to study properties of high-frequency gravitational waves, together with their influence on the cosmological background in which they propagate. It is this non-linear "back-reaction" effect on curvature of the background spacetime which distinguishes the high-frequency approximation scheme from other perturbation methods such as the standard Einstein's linearization of gravitational field in flat space [2,3] or multipole expansions [4] that were developed to describe radiation from realistic astrophysical sources.…”