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Does dark matter act gravitationaly to itself.If Yes, why does not form more compact objects? Can this be explained as its components have enough kinetic energy to overcome the collapse?

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Yes, dark matter acts on itself via gravity, why wouldn't it. It can't form compact objects because it can't shed angular momentum, as explained here: If dark matter only interacts with gravity, why doesn't it all clump together in a single point?

rfl
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  • Shouldn't it be able to shed angular momentum via gravitational waves? – Ryan_L Sep 15 '21 at 21:46
  • Yes but that's utterly negligible. The dominant effect comes from three-body interactions ("swing-by") and even that is very inefficient – rfl Sep 16 '21 at 07:35