Does gravity bend gravity?
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Let's say that there is a large mass $M$ a light-year or so away from a black hole merger, which causes a very large gravitational wave to be produced. When the gravitational wave reaches $M$ , does it bend like light bends when it comes into a curved spacetime?
If you were to think of this situation in terms of quantum gravity, where the gravitational wave is a wave of gravitons, then if gravity does bend gravity, then gravity would be a self-interacting quantum field like the Higgs field?
The short answer is yes, it does. You can find a whole chapter on this phenomenon in Misner, Thorne, and Wheeler's text "Gravitation".
