# metamaterials for gravitational waves

Is there such a thing as refractive index of a material for gravitational waves ? How would the index of a material depend on density - Say density of interstellar cloud vs planet vs star vs neutron star vs black hole ? Could you get an object with negative refractive index - What would this do to a gravitational wave ?

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For a discussion of the optics of gravitational waves in matter, see Ingraham, "Gravitational waves in matter," GRG 29 (1997) 117. You can find a freely downloadable pdf by googling. Since a typical gravitational wave from astrophysical sources has a frequency of ~1 Hz, its wavelength is going to be $\sim10^8$ meters, which means that no foreseeable technology could make a metamaterial. Even if you could, the index of refraction's difference from 1 would be incredibly small. Ingraham derives a relationship $n=1-4\pi G\chi$, where $\chi$ is a susceptibility, basically defined in terms of how much stress-energy tensor you get for a given amount of Weyl curvature. Ingraham suggests that the best chance for seeing the phenomenon might be in "gravitational wave propagation through molecular gas clouds of galactic or intergalactic size." Although $n-1$ would be incredibly small, he suggests that you might be able to see an effect accumulated over thousands or millions of light-years.