As far as we can tell, the interaction between baryonic matter and Dark Matter is strictly a gravitational relationship. Dark Matter would obey the same gravitational laws of physics that normal matter would, in the presence of a black hole. There seems to be no evidence that Dark Matter interacts with baryonic matter or light, in any other way besides through gravity.
Dark Matter would fall (not get sucked in) towards the black hole, because it would follw that curvature... and the black hole would follow the curvature created by the Dark Matter as well. But since Dark Matter is roughly evenly distributed throughout a galaxy, the curvature caused by it might be equal in all directions from the black hole (assuming something like a supermassive black hole, which we see at the core of many large galaxies.) Now we get into orbital velocity and distance parameters, if Dark Matter even has such motions... it appears roughly homogeneous throughout large galaxies, so it would be difficult to use a two-body physics equation for how Dark Matter would fall into a black hole, or if it remained far enough away and had the required velocity at such a distance to not fall in. Because it seems like we cannot assume Dark Matter as a point source of mass (like we can with most orbit equations), the answers to your additional details allude me.
Dark Matter would fall (not get sucked in) towards the black hole, because it would follw that curvature... and the black hole would follow the curvature created by the Dark Matter as well. But since Dark Matter is roughly evenly distributed throughout a galaxy, the curvature caused by it might be equal in all directions from the black hole (assuming something like a supermassive black hole, which we see at the core of many large galaxies.) Now we get into orbital velocity and distance parameters, if Dark Matter even has such motions... it appears roughly homogeneous throughout large galaxies, so it would be difficult to use a two-body physics equation for how Dark Matter would fall into a black hole, or if it remained far enough away and had the required velocity at such a distance to not fall in. Because it seems like we cannot assume Dark Matter as a point source of mass (like we can with most orbit equations), the answers to your additional details allude me.
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Black holes if they exist are invisible thus dark matter is also invisible.
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There is no answer fo this just intelligent speculation, as the existence of dark matter has not been proved. It was created as a necessity as theoretical physicists ran calculation and found out that the mass of the solar system was twice as heavy as they thought hence - dark matter.
I remain skeptical of the concept until further proof has been put forward for its existence, although i do feel it is the marginally the best theory we have to offer for this discrepancy.
i have added two articles which differ in opinion of how black holes interact(or not) with dark matter, to give an idea of how divided the scientific community is about this issue.
take a look at the 'alternative theories' section in the wikipedia article below, before you become to used to idea of dark matter.
I remain skeptical of the concept until further proof has been put forward for its existence, although i do feel it is the marginally the best theory we have to offer for this discrepancy.
i have added two articles which differ in opinion of how black holes interact(or not) with dark matter, to give an idea of how divided the scientific community is about this issue.
take a look at the 'alternative theories' section in the wikipedia article below, before you become to used to idea of dark matter.
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I believe dark matter would respond in the same way as visible matter. Dark matter as I understand it is not anti-matter its only matter not seen. So it should fall into the black hole and become compressed into the singularity thats supposed to be at the center.