Big black holes: an alternative formation hypothesis.

[halfeye]

I was just reading this:

https://www.syfy.com/syfy-wire/bad-a...n-eating-stars

When the thought came to me that it doesn't have to be that way. A black hole becomes less dense as it gets bigger, to the point that it's possible, if enough stars collected closely enough together, that an event horizon could form around them even though there was no black hole present before hand.

[McGarnagle]

Individual stars don't have event horizons. How does a stellar cluster, which would have empty space (or close enough for this discussion) between its constituent stars form an event horizon?

[Anymage]

I'm reminded of the physics factoid that if you were able to cram all the energy in the visible universe down to a point, you'd have a black hole with an event horizon the size of the visible universe. It would create some novel physics if we could prove for a fact that we did in fact live within a black hole (largely in that it would prove certain multiverse/expansive cosmologies true), but we don't see ourselves inexorably drawn to a central singularity or experience any of the other experiences we'd expect to see falling into a black hole.

Since we do see large scale star clusters that aren't black holes despite the fact that they'd all fit into one if you crushed all their mass down together, you'd have to explain why these diffuse clusters become supermassive black holes while others that would fit your definition don't.

[halfeye]

I'm reminded of the physics factoid that if you were able to cram all the energy in the visible universe down to a point, you'd have a black hole with an event horizon the size of the visible universe. It would create some novel physics if we could prove for a fact that we did in fact live within a black hole (largely in that it would prove certain multiverse/expansive cosmologies true), but we don't see ourselves inexorably drawn to a central singularity or experience any of the other experiences we'd expect to see falling into a black hole.

That's the factoid I'm going from, more or less.

Since we do see large scale star clusters that aren't black holes despite the fact that they'd all fit into one if you crushed all their mass down together, you'd have to explain why these diffuse clusters become supermassive black holes while others that would fit your definition don't.

It would be because they aren't all crushed together that they don't all crush together. I am suggesting that maybe, sometimes, a bunch of stars that are close together bunch up a bit in their orbits, and suddenly event horizon. We know that when a black hole forms it's from the outside in. We know that because micro black holes evaporate in Hawking radiation very very rapidly, so if they started small and grew, the explosion would stop the growth.

[Rydiro]

I was just reading this:

https://www.syfy.com/syfy-wire/bad-a...n-eating-stars

When the thought came to me that it doesn't have to be that way. A black hole becomes less dense as it gets bigger, to the point that it's possible, if enough stars collected closely enough together, that an event horizon could form around them even though there was no black hole present before hand.

I'm pretty sure that it is not that simple.(Trademark)
I guess crunching the numbers in general relativity gives you the results that such a constellation would be instable and be crushed into a ring singularity. That's just a guess though, Im no physicist.

[Lord Torath]

I'm reminded of the physics factoid that if you were able to cram all the energy in the visible universe down to a point, you'd have a black hole with an event horizon the size of the visible universe.

That's the factoid I'm going from, more or less.

How reliable is that factoid? Has anyone done the math?

Or is this something along the lines of "Humans only use 10% of their brains" and "Penguins have over 100 feathers per square centimeter of skin"? You know, something that everyone knows is true, despite the fact that they're demonstrably not.

[gomipile]

Since we do see large scale star clusters that aren't black holes despite the fact that they'd all fit into one if you crushed all their mass down together, you'd have to explain why these diffuse clusters become supermassive black holes while others that would fit your definition don't.

But no such clusters have been observed which "all fit" into a black hole whose event horizon would engulf their observed collection of positions. If they did, that would violate Birkhoff's theorem, disproving General Relativity at large scales.

[halfeye]

How reliable is that factoid? Has anyone done the math?

Or is this something along the lines of "Humans only use 10% of their brains" and "Penguins have over 100 feathers per square centimeter of skin"? You know, something that everyone knows is true, despite the fact that they're demonstrably not.

That bit about human brains is a mis-understanding or a mis-communication, not a direct untruth, though there certainly might be an intention to deceive in there. The human brain is made up of two sorts of cells in the main, neurons and glial cells. The neurons do the thinking, the glial cells are there to support the neurons, there are about 10 glial cells for every neuron, so you do only think with about 10% of your brain, but the other cells aren't for thinking with and can never be used for thinking with.

While glia were thought to outnumber neurons by a ratio of 10:1, recent studies using newer methods and reappraisal of historical quantitative evidence suggests an overall ratio of less than 1:1, with substantial variation between different brain tissues.[

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

So that's me out of date then.

On the black holes, it is known that as black holes become more massive, their density goes down. Sagittarius A* has a mass of 4 million Suns, but you could fit the volume required for 4 million Suns into that volume, the stars would do something dramatic if you did, but there is enough space there for them. We can tell there aren't 4 million Sun mass stars at the location of Sagittarius A* because they would be brighter than it is.

But no such clusters have been observed which "all fit" into a black hole whose event horizon would engulf their observed collection of positions. If they did, that would violate Birkhoff's theorem, disproving General Relativity at large scales.

I looked that up on Wikipedia, and I'm not seeing how it applies. I wouldn't expect to see such a cluster because if it came to that point it would disappear behind an event horizon, in an instant.

I hope we can agree that when a stellar mass black hole comes into being in a supernova, the event horizon first forms around a significant percentage of the eventual black hole's mass.

[Lord Torath]

Well, not quite. The radius of the sun is 432,450 km, so the volume of the sun is 1.08 km³ 3.39x10¹⁷ km³ (https://www.space.com/17001-how-big-...f-the-sun.html). Times that by 40 million and you get 4.31x10²⁴ km³ 1.36x10²⁵ km³.

The radius of a 40-million-solar-mass black hole is 118 million km (https://www.omnicalculator.com/physi...zschild-radius), which gives a volume of 2.2x10²⁴ km³, so roughly half the volume.

That said, I see what you mean. Double the mass to 80 million and they're roughly the same volume (the black hole is slightly larger). Increase again, and the volume of the black hole is substantially less dense than a similar mass of sun-like stars all jammed together.

[NichG]

Individual stars don't have event horizons. How does a stellar cluster, which would have empty space (or close enough for this discussion) between its constituent stars form an event horizon?

The Schwarzchild radius is linear in the mass contained within it, but at constant density the mass contained within a volume of a certain radius goes as the cube of that radius. So the density of material needed to have the Schwarzchild radius lie outside of an object's volume decreases as the object's size increases.

So there is some distance scale over which a localized cloud of interstellar medium would have a Schwarzchild radius that lies outside of the radius of that cloud. We can figure that scale out...

The density of interstellar medium seems to vary quite a lot. The high end is ~10^-21 kg/m^3, while the low end is 10 orders of magnitude lower. The Schwarzchild radius is 2GM/c^2, so the radius of a sphere of interstellar medium surrounded by perfect vacuum such that its Schwarzchild radius would be just on its surface would be:

r = 2*G*(4/3 pi r^3 * rho)/c^2

r = sqrt(3*c^2/(8*pi*G*rho))

That gives me r ~= 4 * 10^23 meters, or about 100 million light years, for the high end of interstellar medium density. The size of the observable universe is actually larger than this by about two orders of magnitude, which is sort of surprising to me. On the other hand, at the low end, you'd have a radius 5 orders of magnitude larger (because of the sqrt), which is about 3 orders of magnitude larger than the observable universe. Kind of neat that the extremes bracket the size of the universe like that.

[crayzz]

Orbital velocity is roughly on par with escape velocity, isn't it? It's smaller, but not an order of magnitude smaller in most cases. If you have a stellar system which, as a whole, creates an even horizon that extends beyond the system, then the stars at the edge of the system would have to be traveling at roughly 2c/3, and stars further in would have to be traveling beyond c. You'd have to have all the stars at the edge of the system, all far away from the barycenter.

[Radar]

How reliable is that factoid? Has anyone done the math?

Or is this something along the lines of "Humans only use 10% of their brains" and "Penguins have over 100 feathers per square centimeter of skin"? You know, something that everyone knows is true, despite the fact that they're demonstrably not.

There is linked scientific paper on the star cluster observations here. More sources on the theoretical calculations are within.

The Schwarzchild radius is linear in the mass contained within it, but at constant density the mass contained within a volume of a certain radius goes as the cube of that radius. So the density of material needed to have the Schwarzchild radius lie outside of an object's volume decreases as the object's size increases.

So there is some distance scale over which a localized cloud of interstellar medium would have a Schwarzchild radius that lies outside of the radius of that cloud. We can figure that scale out...

The density of interstellar medium seems to vary quite a lot. The high end is ~10^-21 kg/m^3, while the low end is 10 orders of magnitude lower. The Schwarzchild radius is 2GM/c^2, so the radius of a sphere of interstellar medium surrounded by perfect vacuum such that its Schwarzchild radius would be just on its surface would be:

r = 2*G*(4/3 pi r^3 * rho)/c^2

r = sqrt(3*c^2/(8*pi*G*rho))

That gives me r ~= 4 * 10^23 meters, or about 100 million light years, for the high end of interstellar medium density. The size of the observable universe is actually larger than this by about two orders of magnitude, which is sort of surprising to me. On the other hand, at the low end, you'd have a radius 5 orders of magnitude larger (because of the sqrt), which is about 3 orders of magnitude larger than the observable universe. Kind of neat that the extremes bracket the size of the universe like that.

High-end density interstellar medium is far more than the average density of the observable universe as the matter between galaxies is decidedly more sparse. On those scales one would also need to include the cosmological constant (which as far as I remember is considered to be non-zero), so instead of Schwarzcshild metric, one would use de Sitter-Schwarzschild metric which so far does not have an explicit solutions, but there are reasonable approximations and there is obviously a numeric way.

[Yora]

While I agree with the conclusion that a large number of main sequence stars in a very small area should form an event horizon around them, the density of stars inside that volume would be ridiculously high.
The largest black holes, and therefore least dense, have been estimated to have masses of tens of billions of suns. That's would be several percent of the mass of our galaxy, and that includes the dark matter. And illustrations showing those hypermassive black holes compare them to the size of our whole solar system, but that's still much smaller than 1 qubic light year.
That amount of stars in such a small amount of space, assuming they all orbit their shared center if gravity, should lead to lots of collisions, forming hypermassive stars that collapse into black holes very quickly. It seems much more likely that you would have a central black hole forming first, and then growing outward as more and more stars get shred and fall in. Ar a certain scale the tidal forces should be low enough that stars pass the event horizon intact, but then they would still encounter the chaos inside.

[NichG]

High-end density interstellar medium is far more than the average density of the observable universe as the matter between galaxies is decidedly more sparse. On those scales one would also need to include the cosmological constant (which as far as I remember is considered to be non-zero), so instead of Schwarzcshild metric, one would use de Sitter-Schwarzschild metric which so far does not have an explicit solutions, but there are reasonable approximations and there is obviously a numeric way.

Makes sense. Was more about thinking in terms of scaling laws - the thing that determines whether there'd be an event horizon isn't a critical density, but rather its (at least for Schwarzchild) a critical value of r*sqrt(rho), which is a weird sort of quantity, units of (M/L)^1/2... I wonder if that scaling would be the same or different for other metrics. I suppose if you had line-like, plane-like, or fractal mass distributions, that should change the scaling law.

[Lord Torath]

While I agree with the conclusion that a large number of main sequence stars in a very small area should form an event horizon around them, the density of stars inside that volume would be ridiculously high.
The largest black holes, and therefore least dense, have been estimated to have masses of tens of billions of suns. That's would be several percent of the mass of our galaxy, and that includes the dark matter. And illustrations showing those hypermassive black holes compare them to the size of our whole solar system, but that's still much smaller than 1 qubic light year.
That amount of stars in such a small amount of space, assuming they all orbit their shared center if gravity, should lead to lots of collisions, forming hypermassive stars that collapse into black holes very quickly. It seems much more likely that you would have a central black hole forming first, and then growing outward as more and more stars get shred and fall in. Ar a certain scale the tidal forces should be low enough that stars pass the event horizon intact, but then they would still encounter the chaos inside.

Further along these lines, the Black Hole Calculator I linked above says that for a black hole with the mass of the entire Milky Way (1.9 trillion solar masses - 1.9e12) the Schwarzchild Radius is 0.6 light years. So yeah, I am not surprised that we don't get dense clusters spontaneously forming into black holes.

[Quizatzhaderac]

How reliable is that factoid? Has anyone done the math?

People have. However, I'd include two caveats:

1) There's significant uncertainty about the density of the universe. So "equals" means that the range of uncertainty of the universe size and density could match up this way, and it's a matter of interpretation is proximity is coincidence or a match. There's also the matter of how one factors inflation into things, as the main black hole models ignore inflation and inflation is clearly an important thing the visible universe.

2) Physicists/cosmologists don't seem to often think that this is that profound of a fact. There's not really anything to test if this is true or not and imagining the universe as a white hole^* doesn't really simplify any analysis/model of the observable universe.

*If anything the universe would have to be a white hole and stuff is clearly leaving and unable to come back.

[gomipile]

There's also the matter of how one factors inflation into things, as the main black hole models ignore inflation and inflation is clearly an important thing the visible universe.

Do you mean inflation, the accelerating expansion of the universe, or both?

[Chronos]

Neglecting the cosmological constant / dark energy / quintessence / whatever the Hell you want to call it, the condition for the Universe to be a black hole is exactly the same as the condition for the Universe to be closed. The "Big Crunch" singularity at the end of time would be the singularity at the center of the black hole (note: This is not an analogy; it actually would be literally the same singularity).

But of course, the dark energy is one heck of a thing to neglect, considering that it seems to be over two thirds of the "stuff" in the Universe. And the Schwarszchild-deSitter metric is, well, more complicated, such that it's difficult to make any sort of glib statements about it, in non-mathematical language (heck, hard enough even in mathematical language).

Back to the OP, yes, it would be possible for a sufficiently large and dense star cluster to become a black hole, but it would have to be ludicrously large and dense, far beyond any of the clusters we've ever seen.

[halfeye]

Well, not quite. The radius of the sun is 432,450 km, so the volume of the sun is 1.08 km³ (https://www.space.com/17001-how-big-...f-the-sun.html). Times that by 40 million and you get 4.31x10²⁴ km³.

The radius of a 40-million-solar-mass black hole is 118 million km (https://www.omnicalculator.com/physi...zschild-radius), which gives a volume of 2.2x10²⁴ km³, so roughly half the volume.

That said, I see what you mean. Double the mass to 80 million and they're roughly the same volume (the black hole is slightly larger). Increase again, and the volume of the black hole is substantially less dense than a similar mass of sun-like stars all jammed together.

Unfortunately, it seems I'm wronger than that. Sgr A* is 4,000,000 times the mass of the Sun, not 40,000,000 times. I presume there's a typo on the volume of the sun, but the volume of the 40 million seems plausible.

Further along these lines, the Black Hole Calculator I linked above says that for a black hole with the mass of the entire Milky Way (1.9 trillion solar masses - 1.9e12) the Schwarzchild Radius is 0.6 light years. So yeah, I am not surprised that we don't get dense clusters spontaneously forming into black holes.

Back to the OP, yes, it would be possible for a sufficiently large and dense star cluster to become a black hole, but it would have to be ludicrously large and dense, far beyond any of the clusters we've ever seen.

It wouldn't happen often, and it wouldn't be obvious afterwards that it had, if the cluster hadn't been seen beforehand.

Still, it seems it can't be a general explanation for SMBHs, so that's over.

I may have been mis-remembering this:

The mass of Sagittarius A* has been estimated in two different ways:

Two groups—in Germany and the U.S.—monitored the orbits of individual stars very near to the black hole and used Kepler's laws to infer the enclosed mass. The German group found a mass of 4.31±0.38 million solar masses,[35] whereas the American group found 4.1±0.6 million solar masses.[33] Given that this mass is confined inside a 44-million-kilometre-diameter sphere, this yields a density ten times higher than previous estimates.

as referring to the schwartzchild diameter? Or maybe this:

As of 2020, S4714 is the current record holder of closest approach to Sagittarius A*, at about 12.6 AU (1.88 billion km), almost as close as Saturn gets to the Sun, traveling at about 8% of the speed of light.

Or maybe this image?

Spoiler

Show

Anyhow, I should have checked and I didn't and I'm sorry for the wild goose chase.

[Bohandas]

I'm reminded of the physics factoid that if you were able to cram all the energy in the visible universe down to a point, you'd have a black hole with an event horizon the size of the visible universe. It would create some novel physics if we could prove for a fact that we did in fact live within a black hole (largely in that it would prove certain multiverse/expansive cosmologies true), but we don't see ourselves inexorably drawn to a central singularity or experience any of the other experiences we'd expect to see falling into a black hole.

There is the big bang singularity. And in the opposite temporal direction there seems to be a tendency toward maximum entropy, which could correspond to an event horizon

[Yora]

Further along these lines, the Black Hole Calculator I linked above says that for a black hole with the mass of the entire Milky Way (1.9 trillion solar masses - 1.9e12) the Schwarzchild Radius is 0.6 light years. So yeah, I am not surprised that we don't get dense clusters spontaneously forming into black holes.

It's good to remind yourself from time to time that black holes don't just have Ridiculous Density, but Ludicrous Density.

[halfeye]

It's good to remind yourself from time to time that black holes don't just have Ridiculous Density, but Ludicrous Density.

Depends where you measure the density; the singularity is infinitely dense, however, if you divide the mass by the volume inside the event horizon, then small ones have preposterous density, but big ones don't:

Since the average density of a black hole inside its Schwarzschild radius is inversely proportional to the square of its mass, supermassive black holes are much less dense than stellar black holes (the average density of a 10^8 M☉ black hole is comparable to that of water).

[Radar]

It's good to remind yourself from time to time that black holes don't just have Ridiculous Density, but Ludicrous Density.

As long as they will not go into plaid, we should be fine.

[McGarnagle]

The Schwarzchild radius is linear in the mass contained within it, but at constant density the mass contained within a volume of a certain radius goes as the cube of that radius. So the density of material needed to have the Schwarzchild radius lie outside of an object's volume decreases as the object's size increases.

So there is some distance scale over which a localized cloud of interstellar medium would have a Schwarzchild radius that lies outside of the radius of that cloud. We can figure that scale out...

The density of interstellar medium seems to vary quite a lot. The high end is ~10^-21 kg/m^3, while the low end is 10 orders of magnitude lower. The Schwarzchild radius is 2GM/c^2, so the radius of a sphere of interstellar medium surrounded by perfect vacuum such that its Schwarzchild radius would be just on its surface would be:

r = 2*G*(4/3 pi r^3 * rho)/c^2

r = sqrt(3*c^2/(8*pi*G*rho))

That gives me r ~= 4 * 10^23 meters, or about 100 million light years, for the high end of interstellar medium density. The size of the observable universe is actually larger than this by about two orders of magnitude, which is sort of surprising to me. On the other hand, at the low end, you'd have a radius 5 orders of magnitude larger (because of the sqrt), which is about 3 orders of magnitude larger than the observable universe. Kind of neat that the extremes bracket the size of the universe like that.

Fair enough, I'll concede the soundness of this calculation, but I will refine my objection to point out that this object, at the tippy-top of the density range, would have a mass of about 10^20 solar masses, which is about 0.1% of the mass of the observable universe. My original objection should have included a reference to the mass available within a single galaxy. There just isn't enough stuff in a galaxy for this to happen.

[Tyndmyr]

How reliable is that factoid? Has anyone done the math?

Or is this something along the lines of "Humans only use 10% of their brains" and "Penguins have over 100 feathers per square centimeter of skin"? You know, something that everyone knows is true, despite the fact that they're demonstrably not.

It might be at the right approximate scale, but I don't believe it could possibly be a universal rule, thanks to expansion.

If no new mass is getting created, and it is difficult to see how it constantly would be, the existence of white holes or similar being purely theoretical and unobserved, then mass cannot be keeping pace with the expanding universe, and no persistent relationship exists.

We can extrapolate along existing trends, and see that in a heat death scenario, the relationship cannot hold true. Density isn't a universe-wide constant.

[Yora]

Depends where you measure the density; the singularity is infinitely dense, however, if you divide the mass by the volume inside the event horizon, then small ones have preposterous density, but big ones don't:

A whole galaxy compressed to a 1.2 lightyears diameter is still pretty stupendous to me.

The Sun is surrounded by an 8 lighyear diameter sphere with 0 other stars.

[NichG]

It might be at the right approximate scale, but I don't believe it could possibly be a universal rule, thanks to expansion.

If no new mass is getting created, and it is difficult to see how it constantly would be, the existence of white holes or similar being purely theoretical and unobserved, then mass cannot be keeping pace with the expanding universe, and no persistent relationship exists.

We can extrapolate along existing trends, and see that in a heat death scenario, the relationship cannot hold true. Density isn't a universe-wide constant.

Well, the more the universe expands with constant mass, the more black-hole-like it should become rather than less...

However, we're also talking about 'density' as a shorthand, while going to a non-flat metric (I think) means that perceived density actually depends on the reference frame. Maybe that's even the case in a flat metric because of length-contraction...

[Radar]

Well, the more the universe expands with constant mass, the more black-hole-like it should become rather than less...

However, we're also talking about 'density' as a shorthand, while going to a non-flat metric (I think) means that perceived density actually depends on the reference frame. Maybe that's even the case in a flat metric because of length-contraction...

I'm not quite sure if density works like that in any non-flat metric. Distances between points on any manifold are defined uniquely, so I would say, the same would go with surface areas or volumes. If that is true, by extension density calculations should be consistent as well between different observers barring velocity differences between reference frames that could be accounted for by any observer anyway. As long as we talk about a density as measured in an inertial reference frame stationary with respect to the center of mass of the studied object, it should be uniquely defined as far as I understand.

As I do not have experience with dynamic solutions to general relativity equations, I am not sure, how density and related quantities should be defined in such a context.

[halfeye]

If no new mass is getting created, and it is difficult to see how it constantly would be,

It is? New space is being created from nothing, why not new matter? I'm not saying it is, I have no idea, but one way the big bang could go is new space creating new matter that creates new space and so on in a runaway process. The rate of expansion is increasing if I remember rightly, which would fit with a process running away from itself.

[Anymage]

Empty space does contain energy. Dark energy is a form of energy, and the higgs field has a nonzero value too. (I could talk more confidently about this if I had a solid grasp what dark energy is, but it's up there with quantum gravity as things we don't understand.) The fact that empty space has dark energy and the newly created space from dark energy has dark energy itself is why expansion gets faster the farther you go.

However, the energy density of empty space is really low in the overall scheme of things. Otherwise you'd see lots of spontaneously generating black holes in interstellar space, and the gravity from dark energy (which is a form of energy) would overcome its outward pressure. We don't see those things. And while it's possible for quantum fluctuations to create mass, seeing any meaningful amounts be created and persisted is one of those things that's so unlikely that we only expect to see it long after the heat death of the universe. It might kick start a future big bang and might have been responsible for ours, but isn't something that we can expect to refresh the universe as we have it now.