[big 'if'!]
> any material (of any density) can be made a black hole if there is enough of it
There is an awful lot of intergalactic medium out there. It's of "any density" (albeit very low). How come it's not a black hole? Isn't there "enough of it"? (cf. the "missing baryons problem").
There is an awful lot of atomic and molecular hydrogen gas in the Milky Way and practically every other galaxy. In our galaxy it totally dwarfs all the matter in our central black hole, the stellar black holes, and in all the luminous stars combined. Seems like "enough of it". It's of "any density". How come it's not a black hole?
And so forth.
> (actually, one should properly talk about the circumference)
Why? Also, since we're being properly, what's the circumference of a spinning black hole and how does it evolve with the spin parameter?
Extra credit: assume that you mean the mean density of the interior of M87*, how are you arriving at its volume? (You might cast your eyes over Bengtsson & Jakobsson's extension of work on this question by Christodoulou & Rovelli at respectively https://arxiv.org/abs/1502.01907 and https://arxiv.org/abs/1411.2854 -- when you calculate the volumes in a relativistic spirit, the interiors are very large, far too large to support your (commonly used) throwaway line about dense-as-air/less-dense-than-water). Alternatively, what do you think the BH interior modal densities are?
("In their paper CR [Christodolou & Rovelli] estimate that the black hole at the centre of the Milky Way — whose area radius they assume to be not much larger than the distance to the Moon — now contains enough space to fit a million solar systems. A decent estimate for its spin appears to be a/m ≈ 0.9 [5]. It follows that CR overestimate the volume, but only by a factor of 10 or somewhat less". And from CR: "flat space intuition does not apply to the curved geometry inside the hole [...] and the interior volume keeps growing with time").
I of course expect this comment to be thrown into a deep (gravitational) well, actually.
Nothing to do with the missing baryons problem. If you had a large enough cloud of intergalactic matter it would form an event horizon. Obviously “large enough” is larger than the size of our galaxy and logically any existing galaxy .
One theory of how very early SMBHs may have formed is from direct collapse of large but diffuse clouds.
WHIM. Nicastro et al (2018) https://www.nature.com/articles/s41586-018-0204-1 (you can get a PDF at </https://arts.units.it/bitstream/11368/2935866/4/2935866_s415...> or the preprint at <https://arxiv.org/abs/1806.08395> and there is a nice summary at <https://www.esa.int/Science_Exploration/Space_Science/XMM-Ne...> ).
> If you had a large enough cloud of intergalactic matter it would form an event horizon
I assume you mean that you get gravitational collapse and some form of ~ 2GM black hole horizon (pfdietz's "any material (of any density) can be made a black hole if there is enough of it"). Trivially you can get an event horizon by making the cloud a Rindler observer, or even more trivially by making it an Eulerian observer in de Sitter space. So let's think about what makes a diffuse cloud collapse in a universe like ours at a comparable scale factor.
At the GR level (e.g. matter dominated era OS or LTB like versions of Einstein-de Sitter or similar dark energy dominated era approaches) the problem you encounter is that you end up having to exchange matter between the collapsing "large enough" cloud and the expanding radiation (and other FLRW fluid) filled cosmological region in which it is immersed, and you have to keep a check on the false intuition that leaking stress-energy from the nonvacuum cosmological region into the vacuum in the collapsing cloud -> black hole region is OK to stabilize pressure, because that's not what we see.
We could alternatively look at it through the lens of Jeans instability. To get collapse you need undamped perturbations with oscillation length longer than the Jeans length, which increases in proportion to temperature and decreases in proportion to mass density and mean molecular mass. And then you have to avoid fragmentation. Which takes us to...
> direct collapse [SMBHs]
Sure, in z > 15, the metal-poor radiation dominated era or even earlier, it's plausible (but see below). You need to avoid the formation of molecules or the gas will radiatively cool much faster than it will contract, fragment your cloud and drive cluster star formation. Greedy metals (carbon, oxygen) will kill direct collapse dead. More relevantly to a hypothetical cold intergalactic medium, you need a lot of UV (Lyman, Werner) photons to bust up molecular hydrogen. (But as far as we can tell from e.g. <https://savechandra.org/> the actual intergalactic medium is not cold: <https://astronomy.swin.edu.au/cosmos/I/Intergalactic+Medium> and so the Jeans length is lonnnnnnng).
However, if we have a sufficiently large and cold gas cloud in the dark energy dominated era, with quasars dim and distant, how do we keep it from diluting away with expansion or alternatively fragmenting into overdense and underdense regions? I think the inevitable answer is you need higher mass density and not "any density", which was my point.
Now I'll stray from my island of comfort. I don't do galaxy dynamics or formation and evolution, and I think black holes are mostly pretty boring, so the next two paragraphs and the final one are out of my areas of focus, and there are likely to be gaps and errors. For me, this stuff is all the wrong age, the wrong spatial volume, and/or the wrong energy.
> SMBHs ... from direct collapse [again]
DCBHs (if they exist and if they are the missing step in a hierarchical building of SMBHs by z ~ 7; here supermassive means 10^5 M_sun rather than some of the monsters in the local universe) are due to a direct GR instability in supermassive pop III stars, and have masses around 10^5 M_sun. DCBHs are metallicity limited (thermonuclear kablams), with critical metallicity increasing enormously near and above 10^6 M_sun or so.
If we take the lower end of SMBHs at ~ 10^5 M_sun, then you're right that there are theories of how they may have formed from direct collapse of large but diffuse clouds. A number centre on Priyamvada Natarajan. The introduction of Goulding, Natarajan et al. 2023 <https://arxiv.org/abs/2308.02750> on the weirdo UHZ1 (very dust obscured luminosities from <https://savechandra.org/> X-ray and NIRSpec has a very early z ~ 10 SMBH that seems very unusually massive compared to the host galaxy) lists a few: "Theorists have therefore explored alternate seed formation models, with heavier seed BH mass functions (∼ 10^4 M⊙) that could form from the direct collapse of gas in the high redshift Universe (Lodato & Natarajan 2006, 2007; Volonteri et al. 2008; Inayoshi et al. 2022, see for instance)." Natarajan in a nearly-simultaneous paper on UHZ1 <https://arxiv.org/abs/2308.02654> accepts that a 10^4 M_sun heavy seed is sufficient to explain UHZ1's SMBH:host galaxy mass ratio, and of course 10^4 M_sun is within the range for pop III DCBHs.
Context for next paragraph: "larger than the size of our galaxy ... direct collapse of large ... clouds". I apologize if you did not mean to link your second and third paragraphs that way.
I don't know of many ideas that propose direct collapse into SMBHs much above that lower limit. Directly collapsing a dying supergiant star is hard enough, and much of the work is done in the earlier life of the star. Directly collapsing a 10^12 M_sun or heavier cloud without going through star formation (which would fragment and blow apart the cloud through radiative cooling and reheating) is a pretty wild idea!