Robin said:
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In which case it doesn't obey the normal laws of gravity like ordinary matter which falls towards centres of mass thus forming clumps that we call planets, stars, black holes etc.
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George Jones completely answered your question about DM falling into BH, but the general topic of how DM gathers and coagulates is fascinating. According to computer simulations, DM was able to play an important role in structure formation in the early universe
Google "smoot TED" for an 18 minute video talk about this, with good slides and animations.
It is indeed harder for DM (than for ordinary matter) to gather and fall into higher density regions and stay there, bound.
It has to be able to blow off the extra energy, otherwise it will fall into the region of concentration and then just sail right on thru and out again.
Nevertheless DM is able to collect, and the models show it actually being the BASIS of structure formation in the early U! Because there was more of it. According to the model, it was the first to form the wispy cobweb armature of crisscross strands which then permitted ordinary matter to collect. Where DM strands crossed, clusters of galaxies formed. DM curdling provided the seeds of structure. At least that is the story George Smoot tells, and illustrates with computer sims.
So how does DM manage to collapse into higherdensity cobwebby strands? How does some of the infalling stuff manage to blow off excess kinetic energy so that it can stick around?
By gravitational interaction within the DM cloud which randomly drains energy from some of the DM and pumps it into other DM. The loser DM can stay and become bound in the growing structure, the gainer DM sails out of there with an extra kick.
Expansion will eventually cool or drain kinetic even from that (initially hyperactive) portion. So eventually all the DM settles down and participates in structure formation. Expansion is the overall main cooling engine.
That's just an impressionistic take on Nobelist George Smoot's talk at the TED event. Not an expert myself on early U structure formation, all I can do is say that the puzzles are intriguing and the ideas being tried out are exciting. I't a beautiful subject.
I'd encourage anyone to check it out and get acquainted with it.