Are black holes expected to contain the same ratio of dark matter to regular matter as the rest of the universe?

Question

Are black holes expected to contain the same ratio of dark matter to regular matter as the rest of the universe? I've heard that dark matter is distributed in halos around galaxies. Does that make it less likely to be ingested into a black hole?

Answer 1

(Short answer: No, scroll to the last point.)

• It is irrelevant to an external observer whether the matter that fell into the black hole was dark matter or baryonic, by the no hair theorem. The only properties of a black hole from our point of view are mass, electric charge and angular momentum. (But of course we don't understand quantum gravity.)
• From the point of view of matter which has fallen into the black hole, nothing special happens upon crossing the event horizon. This means that dark matter stays dark and baryonic matter stays baryonic when viewed from inside the black hole.
• There is some controversy about how much dark matter exists in the universe. This recent article, for example, indicates in the abstract that more accurate modelling of galactic rotation curves could eliminate a large percentage of the expected non-baryonic dark matter. (Note as @pela indicated in the comments, that this author's papers have not been peer reviewed and could be suspect.) Obviously, the amount of dark matter in the universe would greatly affect the question's answer. I should note that the controversy is mostly composed of a small number of vocal scientists who appear disproportionately in the media. Following the mainstream news science sections, I get the impression that the death of dark matter seems to be announced once a month or so.
• The formation of supermassive black holes is poorly understood. One hypothesis is that they may form by successive merger of stellar mass black holes. As there have recently been gravitational wave observations of such mergers, and as candidates for intermediate mass black holes have also been observed recently, I will assume here that this is how they form and that supermassive black holes are therefore made of roughly the same stuff as stellar mass black holes.
• Black holes lose most of their mass during the formation process. It is important to always keep in mind whether we are talking about the mass of the stellar core which collapsed to form the black hole (this is often the "mass" of a black hole that is referred to when speaking about e.g. the minimum size black hole that can form from core collapse) or the mass of the black hole as seen by a distant observer after the supernova.
• Dark matter particles can not lose much orbital energy by interacting with other matter nor by radiation, therefore will remain in orbit around a black hole rather than falling in, unless they happen by unlikely chance to hit it near the event horizon. This paper indicates that simulated supermassive black holes derive no more than about 10% of their mass from dark matter.

However, it must be said that some scientists suspect that dark matter is made of primordial black holes in the first place. There is also the theory of MACHOs (Massive Compact Halo Objects), that dark matter is composed of large compact bodies such as black holes, but it is believed by most that this theory can not account for the dark matter in the universe.

Answer 2

Dark matter is (thought to be) in halos which extend both to the centers of galaxies and outside most of the normal matter in galaxies (gas, stars, dust). So a black hole inside a galaxy could and undoubtedly will ingest some dark matter. However:

Stellar-mass black holes form from the core-collapse of a massive star. Since stars are almost entirely of regular matter, the initially formed BH remnant would itself have been made almost entirely of regular matter. Such BHs might later grow by accreting gas (e.g., from a close binary companion star), in which case they're gaining mass in the form of regular matter. There would inevitably be some dark matter swallowed by the BH as it orbited within its parent galaxy -- just as the BH would swallow some interstellar dust, for example. But it would still be overwhelmingly formed out of regular matter.

Supermassive black holes in galaxy centers would probably start out from some kind of early-universe collapse of a gas cloud or very massive star, which would again be mostly regular matter. Subsequent growth of supermassive BHs comes primarily from interstellar gas feeding an accretion disk around the BH, plus the occasional star that wanders too close -- so once again it's mostly regular matter that falls in the black hole. (The central regions of galaxies do have some dark matter, but they're dominated by regular matter. Plus, regular matter in the form of gas clouds can easily lose energy via cloud-cloud collisions and sink to the center of the galaxy, where it could feed a supermassive BH; dark matter can't do this.)

(Of course, as user25972 points out, it's largely irrelevant to outsiders like us what kind of matter goes into making a BH. A black hole formed out of dark matter would behave identically to one formed out of regular matter.)