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1] Dark matter:

Let's consider dark matter to be so weakly interacting we can model it as a perfectly non-interacting gas. For even more simplification, let's assume dark matter particles have some thermal equilibrium distribution. (Are these simplifications unappropriate?) So dark matter will then only settle into gravitational wells to the extent that its thermal distribution will allow. So no "clumping", but definitely more dark matter in a galaxy well than in intergalactic space.

Now, if we place a black hole into this gas, all dark matter particles without enough thermal energy to orbit or escape will be eventually consumed. However, since the gas is non-interacting, it can't "bump" other dark matter particles on its way it. So this consuming could be incredibly slow, and self limiting in that many dark matter particles in the galaxy just won't be consumed at all. In this non-interacting limit, it seems dark matter would be slowly "cleaned" from the area by a black hole. Overall leaving the gas slightly hotter than before (since it preferentially devoured the low energy particles).

This process however would have to repeat when galaxies collide. Since the gas consumption is a non-equilibrium process, I'm not sure how to estimate its speed. I also don't know the differential sensitivity of black hole mass measurements in astronomy (maybe wrong word, but what I mean is I don't care about the absolute value as much as how the value changes in time). Can anyone give estimates or insight on whether these effects could be measureable?

Also, if dark matter does self-interact, the growth rate would be even larger. So could black hole growth be used to place limits on dark matter interactions?

2] Higgs

It seems most particle physics measurements are sensitive to the vacuum expectation value, and not the overall energy density of the Higgs. But since it is the vacuum itself (instead of "particles"/excitations) that has this energy density of the Higgs, then the black holes clearing out the region of dark matter particles cannot apply here for the Higgs. It seems the black hole would have to be pulling in extra energy at a rate proportional to its area and the Higgs energy density. Could black hole mass growth be used to therefore place a limit on the Higgs energy density, using current measurements of the higgs vev from particles physics?

3] Dark energy / Cosmological constant

If the accelerated universe expansion is due to a physical field with positive energy density and negative pressure, then it seems GR would dictate that this energy would fall into a black hole along with a free falling observer. This is in contrast to accelerated universe expansion due to a positive cosmological constant, which is just a constant of the universe and not a physical energy density which can fall into a black hole, so the black hole will not grow. Is this logic correct, and could black hole growth (in principle at least) allow one to distinguish between dark energy and a cosmological constant?