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Tangential, and possibly revealing ignorance here. I definitely don't get why clouds of dark matter surrounding galaxies don't fall into the black hole at the center. Dark matter is there to explain why the outer stars of a galaxy rotate faster than expected, but why is dark matter not distributed roughly in the same density distribution as visible matter?

It is presumed that the dark matter also rotates about the galactic center. It can’t fall in, any more than the stars in the galaxy can, because it collectively can’t dump its angular momentum. However, there is controversy whether dark matter can dissipate momentum that is parallel to the rotational axis either by self interaction or by interaction with ordinary matter. If it can, then the distribution of dark matter could resemble a disk, as opposed to a spherical distribution.

Lisa Randall has written a provocative book about this which will answer your question in depth: Dark Matter and the Dinosaurs: The Astounding Interconnectedness of the Universe.

As others have pointed out, if they’re in a stable orbit they won’t fall in (at least not for a very long time), because unlike luminous matter it won’t experience any force other than gravity. If you imagine a dust cloud of luminous matter around a black hole, it will tend to experience frictional heating the closer it gets, there is the chance of a collision or radioactive decay, and other forces acting to draw it in or send it far away. Dark matter won’t do that, it just couples to gravity. Our usual intuition about how a halo of matter behaves has a lot to do with interactions other than gravity. Clumping for example, aggregation and accretion pretty much work because of interactions other than gravity, until a body becomes massive enough.

They do. But there's nothing special about the gravity of a black hole versus the gravity of "ordinary matter". The vast majority of the matter in a galaxy is in orbit and won't get anywhere near close enough to the central black hole to fall into it. This is true of stars, planets, gas, and dust just as it's true of dark matter.

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