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Is dark matter trapped near / in black holes, like regular matter is, or does something different happen with dark matter?

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It interacts gravitationally.That's all there is to it.

There is a big difference though to the way that normal and dark matter interact with black holes - dark matter is far less likely to be captured.

Given two lumps of matter, one normal one dark, with the same mass and angular momentum with respect to the black hole; only the normal matter is capable of shedding its angular momentum (normally an accretion disc is involved), which allows its orbit to shrink enough to be captured (within three Schwarzschild radii). Dark matter is dissipationless; if it has too much angular momentum it won't get captured.

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    $\begingroup$ If the trajectory of a dark matter particle intersects with the event horizon of a black hole, it isn't coming back out, is it? $\endgroup$ – Howard Miller Mar 22 '16 at 3:02
  • $\begingroup$ @HowardMiller Correct. That would be an example of material on an almost radial orbit, with almost no angular momentum. $\endgroup$ – Rob Jeffries Mar 22 '16 at 7:00
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    $\begingroup$ I've read that galaxies tend to be structured with a dark matter halo, less dark matter throughout the stars of the galaxy, then a supermassive black hole at the center. Also, stars and galaxies seem to be located along streamers of dark matter. So I've been wondering if dark matter has a larger role in the formation of galaxies, forming the framework including a supermassive black hole. that becomes a formation of stars later on. The alternative seems that billions of stars collapse to form it. $\endgroup$ – Howard Miller Mar 23 '16 at 6:19

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