If you’re five feet from the surface of the sun you’re hundreds of thousands of miles away from its center of mass. If you’re five feet away from the “surface” of a solar mass black hole you’re just a couple of miles away from the center of mass.

The shape of gravitational field only differs within the body. The shape outside of the perfectly spherical body will be exactly the same regardless of how the mass is distributed (whether it is all on the surface or all in the middle of it).

Or in other words, if you are on the surface of the sun, you will feel exactly the same acceleration as if entire mass of the sun was concentrated in its center.

The only time you feel the difference is if you dip into the sun. As you go deeper and deeper, the pull from all the mass that is further from the center than you are will perfectly nullify each other. As you go deeper and deeper into the sun you will feel less acceleration.

The takeaway is that the cellophane dimple is more warped around the center point, but if, say, our Sun were to suddenly turn into a black hole it wouldn't change anything about our orbit.

Black hole does not have a surface. At least not that we know of. Event horizon is a surface, but it is not the surface of the BH in conventional sense. If you were falling into BH nothing special would happen as you crossed event horizon.

And neither does the Sun. Just like Earth's atmosphere, we can only talk about some arbitrary altitudes or pressures, but reality is that the atmosphere of the Sun or Earth does not have any firm beginning or end. And Sun is all atmosphere.

Is the mass of the black hole perpetually "falling" through spacetime at near the speed of light?

Would the region around an "active" black hole appear more massive when it is consuming matter vs existing in a vacuum?

A big object going really fast would be almost stopped in time, while at the same moment be almost infinitely massive which is increasing the gravitational effect. The combination of these effects is what makes such a big "dent" in spacetime?

There's a whole science to this with a fun name:

https://en.wikipedia.org/wiki/Degenerate_matter

Quantum theory predicts and limits the sorts of things you can get once you really put the squeeze on and these predictions align well with observations.

Black holes and neutron stars are fundamentally different - there’s no space left between the matter of a neutron star. Now, the physics of that is a bit over my head, but a simplification I got from a PBS Spacetime episode is that the matter in a neutron star pretty much overlaps in 3d and stars filling up some quantum mechanics dimensions. When those cross a threshold, the last forces give way and everything collapses without a limit. So now we’re talking about a ball on your cellophane as small as physically possible for its mass (compact), pushing down significantly deeper… Until it gets replaced with pretty much a puncture, pushing it down to some abstract floor.

I think of it like "magnets as rubber bands", and what I call "Feynman lies":

> I can't explain [magnetic] attraction in terms of anything else that's familiar to you. For example, if we’d said the magnets attract like as if they were connected by rubber bands, I would be cheating you. Because they're not connected by rubber bands, I shouldn’t be in trouble, you’d soon ask me about the nature of the bands… and secondly if you were curious enough, you'd ask me why rubber bands tend to pull back together again, and I would end up explaining that in terms of electrical forces, which are the very things that I'm trying to use the rubber bands to explain, so I have cheated very badly, you see.

> [...]

> But I really can't do a good job, any job, of explaining magnetic force in terms of something else that you're more familiar with, because I don’t understand them in terms of anything else that you are more familiar with.

direct link: https://www.youtube.com/watch?v=nYg6jzotiAc&t=1263s

but the whole chapter is worth a watch: https://www.youtube.com/watch?v=nYg6jzotiAc&t=894

I think you're misremembering, we don't know what's at the center of a neutron star, or that there aren't other, more dense, types of stars.

That’s what I get for treating modern physics as a kind of a vaudeville show ;)

> If they have similar masses, how does the black hole bend "deep" enough into space to the point where not even light can escape?

A back hole is smaller ball

Light does not escape in the black hole case because the black hole is smaller: in case of a black hole earth, light starting at 6370 km (current radius) can still escape. A black hole weighing the same as the earth would have a 9 millimeter radius, no light will escape from there.

[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!

This analogy probably is not very good for this kind of things, but it shows the idea.