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I know that dark matter rarely interacts with itself and with ordinary matter. but black holes produce a gravitational field strong enough to curve and drag space-time so shouldn't dark matter also get sucked in being a part of space-time.

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    $\begingroup$ Dark matter is a proposal that attempts to explain things that are not understood of explained with known physics. No one has seen dark matter or explained exactly what it is. It might be correct but it could also be a lot like the ether in that it was widely believed yet ultimately shown to be untrue. $\endgroup$
    – JimmyJames
    Jan 23, 2018 at 14:35

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Dark matter is called 'dark' because it does not interact electromagnetically, so that we actually cannot see it with any of our telescopes. It does however interact gravitationally, and actually that is the main effect that lead to postulating its existence (when looking at rotation of stars around the galaxy, normal matter is not enough and there must be something else). So dark matter would feel the black hole the same way as you would, according to the Equivalence Principle.

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