Sorry if this question is too elementary, as is my level, but I'm wondering how close two supermassive black holes can get and should the Keplerian rotational frequency at that point equal to the frequency of the emitted gravitational wave? I guess I'm asking how the maximal frequency of classical mechanics of this binary system compares to the maximal frequency of the emitted gravitational wave?
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There's some related info about gravitational wave frequency emitted by a binary system here: https://physics.stackexchange.com/q/316798/123208 Analysing the motion of a binary Schwarzchild BH system isn't easy, as discussed here: https://physics.stackexchange.com/q/3612/123208 However, SMBHs tend to have high spin, as discussed here: https://astronomy.stackexchange.com/a/20292/16685 which makes things much trickier. – PM 2Ring Jul 25 '20 at 15:49