How does Dark Matter interact with Quantum Singularities?
Can a DM particle fall inside an event horizon and coast through to the other side?
Supermassive black holes seem to be the nuclei of galaxies…does that tell us something significant about Dark Matter?
“Quantum singularity” is a Trekism, and means absolutely nothing in actual science. I’ll assume you meant to ask about black holes. Black holes are gravitational phenomena, and dark matter is subject to gravity, so (if it hits the event horizon) it’ll get captured, just like anything else.
The catch is that, while black holes can be very massive, they’re also very small. In fact, they’re the smallest thing possible for their mass. So a direct hit is pretty unlikely. With ordinary matter, this isn’t such a big deal: If ordinary matter falls into the general vicinity of a black hole, it’s likely to collide with other ordinary matter falling into the general vicinity, and get caught up in the accretion disk, and hence eventually spiral in. But that won’t happen with dark matter, and so a direct hit is the only way to fall in.
So if a direct hit happens and dark matter falls in, and Hawking radiation happens, can we say that a black hole can convert dark matter into regular matter via Hawking radiation? Does Hawking radiation produce any candidates for dark matter itself?
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Yes, you could convert dark matter to regular matter in that way, though of course it’d be quite slow. And Hawking radiation can produce any sort of particle that interacts gravitationally, i.e., any sort of particle at all, but for a hole of realistic size, the radiation will be very strongly biased to particles with zero or very low mass, and we have strong reason to believe that any dark matter particles we don’t know about have very, very high mass.
You can’t expect to get away with that 
Come on. Why?
If they didn’t, we’d have discovered them already in the same way that we discovered neutrinos: We’d see particle collisions where the initial particles had some amount of energy and momentum, and the outgoing particles we could detect had some amount of energy and momentum, and the two didn’t match, indicating some unseen particle that’s carrying away energy and momentum unnoticed. We now do particle collisions with very high energies, and still haven’t seen this, so any such dark matter particles must have masses higher than the energies we’ve been able to probe.
Well, if they interact with normal-matter particles in any way (including the weak interaction), that is. I suppose that low-mass dark matter particles are still possible, if they’re not even weak. But every single particle we know of is subject to the weak interaction, so that would be at least a little surprising.
Here’s a question: how big (statistically) does a black hole have to be so that the influx of dark matter equals the outflux of Hawking (RIP) radiation. That is, black holes above that size will not evaporate away, at least until the local dark matter density drops.
You’d also have to take into account the background microwave radiation.
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Just FTR, that RIP refers to his death today.
I’ve never seen anyone run the numbers for dark-matter accretion, and it would depend on details of the dark matter like its temperature and the mass of the individual particles, for which we don’t have any very firm numbers. But for the cosmic microwave background, it’s straightforward: A stellar-mass black hole has a temperature of about a millionth of a kelvin, and the CMB has a temperature of a few kelvin, so a black hole would need to be less than a millionth of the mass of a star before it would radiate more than it accretes from the CMB.
The temperature alone is sufficient to do the calculation for the CMB, since it’s made up of massless particles, whose only contribution to energy is from their temperature, but it’s not enough for dark matter, because it’s “cold”, with energy due to temperature being much less than the particles’ mass.