Main Question or Discussion Point
I think i came across this before. Does the size of an object's gravitational field contribute to its gravitational field?
For the cognoscenti, I point out that an arXiv eprint by Costa and Herdeiro, "A gravito-electric analogy based on tidal tensors", offers a thoughtful critical review of some often mentioned mathematical analogies between gtr and EM (in particular, the GEM formalism). This is one of the few eprints I have seen which distinguish clearly between the electro(magneto)gravitic tensor (i.e. the electric(magnetic) parts of the Riemann tensor) and the electric(magnetic) parts of the Weyl tensor, and give some reasons why those in the know prefer the former.The short answer is yes - the long answer involves a lot of cautions about what , if anything, the term "gravitational field" actually means.
So this is just an interpretation of the non-linearity of the left-hand side, and not like a static object's gravitational field grows over time due to this, right?