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I am curious if stars (or other massive bodies) amplify or refract gravitational waves in a manner similar to the following.

Amplification
In the case of amplification, do massive bodies affect gravitational waves similar to the steepening that occurs in shallow water waves during runup near shore? Or can massive bodies act like a pump to locally amplify (or damp) the waves? Propagation of a tsunami offshore, showing the variation of wavelength and amplitude as a function of depth (Courtesy of Régis Lachaume on Wikipedia Commons).

Refraction
In the case of refraction, I am wondering if massive bodies act like (in a very loose, analogous way) obstacles in water for water waves (e.g., see animation below)?  Propagation of periodic waves over an elliptic underwater shoal on a uniform beach. The computations have been made using a Boussinesq-type model, and show the effects of wave refraction, diffraction and shoaling on the wave field (Courtesy of Kraaiennest on Wikipedia Commons).

I realize that gravitational waves are quadrapolar, not mono- or dipolar but I do not think that renders them immune to similar effects if they truly are waves.

Update
After some searching, the closest thing to an answer that I could find was a paper by Peters [1974] that treats the index of refraction for gravitational waves as a scalar, which seems problematic for addressing a quadrapolar mode.

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  • $\begingroup$ This is a cool question. I doubt that something very massive doesn't do something to the waves, but have no idea what. $\endgroup$ – zeta-band Jun 15 '18 at 21:21
  • $\begingroup$ Why would a scalar index of refraction be any more problematic for quadrupole radiation than for a dipole radiation (i.e., Maxwell's equations in matter?) $\endgroup$ – Michael Seifert Jun 15 '18 at 21:52
  • $\begingroup$ @MichaelSeifert - Fair point. I guess I am used to plasmas where the susceptibility is a tensor and the index of refraction is a vector at minimum. $\endgroup$ – honeste_vivere Jun 16 '18 at 18:46
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Do stars amplify or refract gravitational waves?

Not to any extent that could be measured. When a gravitational wave comes to a star, it has traveled a distance of at least on the order of a light-year from the source, so its amplitude is small. The gravitational field of a star is also near the weak-field limit. In the weak-field limit, the Einstein field equations, which are nonlinear, behave approximately linearly. Therefore the field of the star does not interact significantly with the field of the wave.

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