I can see why Dark Matter (DM) is unlikely to form concentrations that would trigger the formation of a "Dark Matter Black Hole" but Dark Matter and Atomic ("normal") Matter (AM) each seem to feel the other's gravitational attraction, which would lead us to suppose that some DM would find is way into Black Holes (BHs). The question is whether DM might behave differently when it enters a BH and whether there might be observable consequences, which might shed some hazy light on the nature of DM. We'd need to find a BH in an area known to be rich in DM and also at an observable distance from Earth.

Odd behaviour might include a change in character of the force of attraction between AM and DM such as becoming repulsive, or being overcome by another force, at short range.

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