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I know that (for example) binary neutron stars can emit radiation in the form of gravitational waves. This question got me thinking about the case of three or more objects. I wrote in my answer that if there were just two black holes in this scenario, the system should submit gravitational waves and undergo orbital decay. I also speculated that this might be the case with 3 or more bodies.

Was I correct? If so, could I use a modified version of the formula I listed for orbital decay to calculate the orbital decay for this n-body system?

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    $\begingroup$ Why would n-body systems not emit gravitational waves if a two-body system does? $\endgroup$
    – CuriousOne
    Commented Oct 18, 2014 at 3:55

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Its almost impossible to have an n body system not create gravitational waves. Natural systems of more than one body will always have a quadropole moment of some sort, along with some angular motion. Then if the entire system is somehow finely balanced, there would certainly be regions in the system radiating GR waves.

Three body (or more) systems can't be reliably modelled using formula and equations, unless you simplify the system to be approximatively a two body one.

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  • $\begingroup$ Even the two-body system isn't easy to model; we can only do an approximate job analytically and we need computers to get through the merger. We can only model the two-body system if we assume that the orbits are quasi-Keplerian, and then gradually build in approximations to corrections from relativity. The main thing that would make it hard to model an $n$-body system in the same way is not the gravitational-wave emission, but the fact that even in Newtonian gravity, $n$-body systems are hard. If you knew the orbits, the approximate gravitational-wave emission would be easy. $\endgroup$
    – Mike
    Commented Nov 6, 2017 at 15:38
  • $\begingroup$ The question is CAN a general n body system emit waves. My answer is they all will except for a vanishingly small set (ie a set of zero measure). $\endgroup$
    – Tom Andersen
    Commented Feb 1, 2018 at 23:57
  • $\begingroup$ Okay. And then there's that last sentence, to which I guess I was responding. $\endgroup$
    – Mike
    Commented Feb 2, 2018 at 2:13

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