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Some people speculate that the mysterious dark matter in the universe could be tiny black holes. But on the other side, could dark matter particles attract each other by gravity and finally form a black hole? Since dark matter is even more abundant than normal matter, the dark matter black hole should not be rare.

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I think the problem with matter that only interacts gravitationally is that it's hard to get it all to stay in one place. Nebula slowly form stars and planets in part because of collisions between particles lead to larger particles, which tend to attract further particles. But particles that just wizz right through each-other can't coalesce without violating conservation of angular momentum. That's not to say that it's impossible, however. Just that the dynamics are different.

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You are right. If dark matter only interact gravitationally, then it's hard for them to accumulate. For example, considering two dark particles, when they "collide"( which means overlapping in space time), they pass through each other. If more particles are added in, a chaotic soup may form. This is much easier to simulate in a computer program. However, whether dark matter really doesn't interact through other forces is not clear. –  Fine Observer Dec 20 '13 at 21:32
    
@FineObserver In fact this is what we observe in gravity-only simulations. When galaxies collide, so do their dark matter halos, but they mostly passes right through each other. This forms large dark matter filaments through and around galaxies. –  Kevin Driscoll Dec 20 '13 at 21:41
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@KevinDriscoll I think you should maybe expand that comment into an answer as it describes explicit simulations that exactly answer the OP's question. Lionel's answer is good, but you're clearly an expert thinking exactly about the OP's question in your day job: it would be great to get such an authoritative answer on this site. Too many of us are generalists and, whilst some of us have excellent physical intuition and give great answers, it's not quite the same. –  WetSavannaAnimal aka Rod Vance Dec 20 '13 at 21:51
    
Here's a synopsis of a Physics review letter on the topic ;-) –  Waffle's Crazy Peanut Dec 21 '13 at 10:10
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