[kune]

The density of black hole decrease by the inverse square of the mass of the black hole. That means massive black holes have a much lower density that small black holes. So they are more likely to form than small black holes. Dark matter will have played an important role in the creation of those early black holes. If there is no dark matter and some form of MOND theory of gravity is correct, the Schwarzschild formula will require a modification for large black holes. In that case galaxy centers will not require large masses to see the same effects.

[Keysh]

That means massive black holes have a much lower density that small black holes. So they are more likely to form than small black holes.

No, it doesn't, because you're ignoring all the physics required to get the mass into a small enough region so that it will collapse to form a black hole. The only way to make that happen that we know works is to form massive stars, where a fraction of the star's mass, in the center of the star, will eventually form a black hole. But the largest stars we know of have masses of ~ 200 times the Sun, and so can't form black holes more than a fraction of that.

If you imagine a more massive gas cloud collapsing under its own gravity, it will fragment into subclumps before getting very dense; these subclumps will themselves fragment or go on to form stars directly, but with an upper limit of, say, ~ 200 solar masses.

(It's possible that if you start with a cloud of pristine gas in the early universe -- nothing but hydrogen and helium -- that it might collapse to form a single supermassive star, or even a black hole directly. That might give you something like a 1000-solar-mass black hole. But that's still fairly speculative, and requires unusual conditions that don't exist generally.)

[sebzim4500]

>So they are more likely to form than small black holes.

This certainly does not follow from the rest of your comment. I'm pretty sure it's false.

[AnimalMuppet]

I think the claim is like this: You have the primordial universe, shortly after the big bang, with fluctuations in density. But the whole density is very high. A fluctuation over a large region could put the region over the threshold to become a black hole, because the density required for that to happen is lower than for a small region.

Mind you, I don't know if this actually works. What was the density of the early universe, compared to the density required to form a black hole? How large were the fluctuations? Is this scenario plausible at all?

I suppose that if you go back close enough to the big bang, then you can get a density high enough. But then, if you go back not much farther, shouldn't the whole universe have formed a black hole? And if it didn't, can we trust the logic that says that the situation should have led to the formation of giant black holes?

[KolenCh]

They may have included the effect of black hole evaporation here? Small black holes evaporates much quicker and won't survive.

[sebzim4500]

I guess, but even a solar mass black hole would take 10^64 years to evaporate

[whimsicalism]

> So they are more likely to form than small black holes.

Based on your previous sentence would it not be the opposite?

[micw]

What exactly is the "density" of a black hole?

As I understand, a BH is a singularity, so all mass is at one point which means all BHs have the same (infinite) density.

Is it a kind of "virtual density", e.g. the mass of the singularity devided by the schwarzschild radius or the event horizon?

[codethief]

I suppose OP defines it as the mass of the BH, divided by the apparent volume taken up by the BH (more precisely: the apparent horizon), as seen from the outside. Put differently, for a Schwarzschild BH: Density ~ M/R³ (modulo constant prefactors) ~ 1/M², since the Schwarzschild radius is linear in M.

[zycon]

Density is mass divided by volume. Volume of BH is defined by event horizon.

Singularity is a result of applying a theory of relativity in a case where we know relativity doesn't work, so it's unlikely it's real.

[codethief]

> Volume of BH is defined by event horizon.

The event horizon is a three-dimensional null hypersurface, though, encompassing a four-dimensional spacetime "volume". You are probably referring to the two-dimensional apparent horizon, which depends on the spatial slicing.