We all know that objects can absorb and reflect electromagnetic waves. It stands to reason the same might be true for gravitational waves.
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1The general term is “scatter”, not “reflect”, for what happens to the parts of the wave that are not absorbed. – G. Smith Mar 03 '21 at 23:24
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2There is extremely little interaction, unless the gravitational wave encounters a black hole. See Can gravitational waves be absorbed near a quasar? and links therein. – mmesser314 Mar 03 '21 at 23:52
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Yes, objects can scatter and absorb gravitational waves.
For example, this paper considers the scattering and absorption of gravitational plane waves by rotating black holes.
And this answer discusses how much energy the Earth absorbs when a gravitational wave passes through it. (It’s miniscule.)
Historically, Feynman’s sticky bead argument helped settle early controversies over whether gravitational waves carried energy that could be absorbed and in principle detected.
G. Smith
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It might be good to highlight that the absorption and scattering rates are generally miniscule (e.g. $10^{-25}$ absorption ratio for a 100 Hz gravitational wave passing through Earth from the answer in the second link). – Emil Mar 04 '21 at 15:07
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3When a detector like LIGO measures a gravitational wave, doesn't some (very miniscule amount) of the wave's energy have to be transformed into the kinetic energy of the detector? – Barmar Mar 04 '21 at 17:07