I How certain are we about black hole mass density?

[hkyriazi]

The Wikipedia entry on "White dwarf" has a table listing the densities (in kg/m³) of various objects/substances, and states that an earth-mass black hole has a critical density of 2 x 10³⁰, about 13 orders of magnitude denser than atomic nuclei. Has such an enormous density been calculated, based on a black hole's observed gravitational pull and its observed (Schwarzschild?) radius, or is this a purely theoretical result? Basically, I'm wondering how certain, if at all, we are that such densities are possible.

 

[Dale]

an earth-mass black hole has a critical density of 2 x 1030, about 13 orders of magnitude denser than atomic nuclei. Has such an enormous density been calculated, based on a black hole's observed gravitational pull and its observed (Schwarzschild?) radius, or is this a purely theoretical result?

This is purely theoretical. It is also one reason why we believe there are no natural earth-mass black holes. A larger black hole has a lower critical density.

 

[Buzz Bloom]

Hi @hkyriazi:

You might want to do a bit of arithmetic. One way to define the density of a black hole is its mass M divided by the volume of a sphere with a radius equal to its Schwarzschild radius r_s.

Wikipedia gives a formula for the Schwarzschild radius as

r_s = 2.95 M/M_sun km.​

https://en.wikipedia.org/wiki/Black_hole#Physical_properties

I was unable to find any usage of he term "critical density" with respect to a black hole except in the table in the article
https://en.wikipedia.org/wiki/White_dwarf .
I do not know the definition of "critical" in this usage.

Regards,
Buzz

 

[Nugatory]

It's a calculation, but the gravitational pull doesn't come into it. If all the mass were not inside the event horizon it wouldn't be a black hole, so knowing the mass and the "volume" from the Schwarzschild radius is enough to calculate the "density". (The scare-quotes around the word "volume" are because we're defining the "volume" of the black hole to be the volume of a sphere whose surface area is $4\pi{R_S}^2$; the actual volume of space inside the event horizon is not well defined.)

 

[PeterDonis]

an earth-mass black hole has a critical density of 2 x 10³⁰

This "density" is just a numerical calculation that assumes that the hole's mass is contained within a Euclidean sphere with the surface area of the hole's horizon. Such a calculation has no physical meaning; it's just a number that pop science treatments sometimes throw out for no good reason. A black hole is not a static object with mass contained in a Euclidean 3-sphere with the surface area of the horizon. It's something very different.

 

[PeterDonis]

It is also one reason why we believe there are no natural earth-mass black holes.

I don't think this is correct. As I said in my previous post, this "density" calculation has no physical meaning. AFAIK it does not play a role in any hypotheses about what masses of black holes we should expect to observe.

 

[hkyriazi]

It's a calculation, but the gravitational pull doesn't come into it.

I assume astronomers have looked at the rotation rates of galactic cores, and calculated central "super-massive black hole" masses based on the gravitational pull apparently exerted. I doubt they're able to visualize the black hole event horizon (due to gravitational lensing?) sufficiently to do a pedestrian density calculation.

 

[hkyriazi]

So, then, is it safe to assume that no pedestrian but respectable, pop science-type calculations have been made of mass densities in black holes, that yield densities much greater than those of neutron star cores?

 

[PeterDonis]

So, then, is it safe to assume that no pedestrian but respectable, pop science-type calculations have been made of mass densities in black holes

You're missing the point. A black hole is not an ordinary object full of matter. It doesn't have a well-defined density at all.

 

[Nugatory]

I assume astronomers have looked at the rotation rates of galactic cores, and calculated central "super-massive black hole" masses based on the gravitational pull apparently exerted. I doubt they're able to visualize the black hole event horizon (due to gravitational lensing?) sufficiently to do a pedestrian density calculation.

It's not necessary to visualize or otherwise measure the size of the event horizon. The Schwarzschild radius is a function only of the mass, so if you know the mass you also know the "volume" and hence the density.

Note also that the "volume" goes up as the cube of the Schwarzschild radius while the Schwarzschild radius is directly proportional to the mass. Thus the "density" goes as the inverse square of the mass; an earth-mass black hole may be 13 orders of magnitude denser than an atomic nucleus, but a supermassive black hole is less dense than ordinary boring room temperature water. Thus, no extraordinary mechanisms are needed to turn a sufficiently large amount of gas into a supermassive black hole; its own ordinary gravitational attraction is enough to compress it to below the Schwarzschild radius and form the black hole.

 

[PeterDonis]

no extraordinary mechanisms are needed to turn a sufficiently large amount of gas into a supermassive black hole; its own ordinary gravitational attraction is enough to compress it to below the Schwarzschild radius and form the black hole

I don't think this intuitive reasoning is correct, because, as I've already said, the "density" calculated this way has no physical meaning. Even if we are considering a vast cloud of gas, if it is true that "its own ordinary gravitational attraction" is enough to cause it to become a black hole, then its spacetime geometry is already sufficiently different from flat that its density, even before it forms the hole, can't be calculated by assuming it is occupying a Euclidean volume of space bounded by its surface. So I don't think any intuitions along these lines should be used.

 

[pervect]

The density (usually of a presureless cloud of "dust") to form a black hole of a given size/mass is well defined though, and I believe is what the popularizations are calculating.

It'd be more interesting (but more complicated) to consider some sort of idealized fluid model that represented matter, and calculate the amount of pressure needed to compress an Earth-sized cloud of this idealized fluid to a low enough volume for it to form a black hole.

The usual model would be degenrate matter, <<wiki link>>

I don't know the experimental bounds on our understanding of neutron degenreate matter (the most reasonable case for a small black hole) would be though. I don't think they're terribly tight, but I'd be surprised if we didn't at least know the correct order of magnitude - at a guess.

 

[PeterDonis]

The density (usually of a presureless cloud of "dust") to form a black hole of a given size/mass is well defined though

Only in the sense that, in an idealized model such as the Oppenheimer-Snyder model of collapse of dust, given an externally measured mass (which is constant throughout the process), and an initial radius for the object when it starts collapsing from rest (which must be at least 9/8 of the Schwarzschild radius for the given mass because of Buchdahl's Theorem, and in practice will be much larger), one can calculate the density of the dust (which is uniform throughout the dust) at the instant when it is just crossing the event horizon of the spacetime as it collapses. But this density is not the same as the density being calculated by these pop science calculations. It is also not "the density of the black hole" in any meaningful sense. Nor is it the density of the dust when it starts collapsing from rest (that will be smaller).

It'd be more interesting (but more complicated) to consider some sort of idealized fluid model that represented matter, and calculate the amount of pressure needed to compress an Earth-sized cloud of this idealized fluid to a low enough volume for it to form a black hole.

This would be relevant for primordial black hole formation (i.e., formation by pressure and density fluctuations in the early universe), but not for formation of black holes by gravitational collapse. Such a collapse does not involve "pushing matter inward" by pressure.

I don't know the experimental bounds on our understanding of neutron degenreate matter

As far as the densities we have a reasonable understanding of? IIRC we have a reasonable approximate model of the equation of state of neutron degenerate matter up to about a hundred times nuclear densities, or about $10^{18} \text{kg/m^3}$.

 

[sweet springs]

A black hole is not a static object with mass contained in a Euclidean 3-sphere with the surface area of the horizon. It's something very different.

May be it is along the line with this that I once calculated the integration of energy momentum pseudo tensor t in region outside Schwartzshild boundary sphere of BH. I got the result equals Mc^2 where M is mass of BH. It could be interpreted that all energy exist outside Schwatzshild sphere, not inside.

 

[bobob]

The Wikipedia entry on "White dwarf" has a table listing the densities (in kg/m³) of various objects/substances, and states that an earth-mass black hole has a critical density of 2 x 10³⁰, about 13 orders of magnitude denser than atomic nuclei.

That statement is somewhat misleading. The matter within the black hole has collapsed completely, so aside from any matter falling into a black hole, the interior doesn't contain any matter. All of the matter ends up at the singularity and the interior is just empty space. It would be more accurate to just state the schwarzschild radius of a black hole having the mass of the Earth and leave it at that. A better way to understand this is to ask why all matter doesn't end up in black holes and why there are any objects that have the densities like that of white dwarf stars. The answer to that requires more than just general relativity and the relationship you get between a black hole mass and its corresponding schwarzschild radius.

What gives a white dwarf such a large density is what prevents it from collapsing any further and that is due to quantum mechanics and forces other than gravity. In particular, there is a limit to the number of particles you can confine to a given volume due to the exclusion principle. this results in a pressure that resists gravity trying to squeeze those particles into a smaller volume. Finding out the volume at which the pressure balances gravity requires knowing something called the density of states, which depends on things other than just mass and volume. You can look up Chandrasekhar limit to see how this is obtained for a white dwarf and Oppenheimer-Volkoff-Tolman limit for neutron stars. Whether or not further collapse into a more dense, stable body (like a strange star made of uds quarks) is possible is an open question. In any case, the density of matter alone is not sufficient determine whether or not the matter will further collapse. You have to know what is preventing matter from collapsing which requires knowing the number of quantum mechanical states available to the particles confined to that volume.

Has such an enormous density been calculated, based on a black hole's observed gravitational pull and its observed (Schwarzschild?) radius, or is this a purely theoretical result? Basically, I'm wondering how certain, if at all, we are that such densities are possible.

The density of a neutron star (which is much denser than a white dwarf) is certainly possible because the density of a neutron star is not estimated to be that much different than the density of your average heavy nucleus. Lots of experiments have been done to determine nuclear densities, so a density on the order of 10^17 kg/m^3 is not just a theoretical result. One of the reasons nuclear physicists study nuclei is to better understand nuclear matter and refine the equation of state for nuclear matter and consequently for understanding neutron stars and how large they can be without collapsing further.

 

[Dale]

I don't think this is correct. As I said in my previous post, this "density" calculation has no physical meaning. AFAIK it does not play a role in any hypotheses about what masses of black holes we should expect to observe.

I disagree. We don’t know of any natural process which will take an isolated Earth mass and compress it to a density ~13 times the density of atomic nuclei. We do know of natural processes which will take an isolated million solar mass and compress it to the density of water. Therefore we expect to see million solar mass black holes but not Earth mass black holes.

If an amount of matter is uniformly distributed throughout its schwarzschild radius then it is already a black hole fully inside its event horizon. It will of course not remain uniformly distributed, but it is a perfectly valid initial condition that gives an easy plausibility check.

Leonard Susskind uses this type of argument in his GR course.

 

[PeterDonis]

I once calculated the integration of energy momentum pseudo tensor t in region outside Schwartzshild boundary sphere of BH

A black hole is vacuum everywhere, outside and inside, so this integral will give zero. If you got M, you did it wrong.

 

[PeterDonis]

We do know of natural processes which will take an isolated million solar mass and compress it to the density of water.

We know of natural processes which will take a million solar masses worth of highly diffuse matter and have it eventually collapse to a black hole whose "density", if it is calculated using the physically meaningless method described earlier, comes out to the density of water. But, as I've already said several times, this "density" is physically meaningless, and the process is not a process of anything being "compressed". It's gravitational collapse, which is something different.

Also, as I've already said, the physically meaningless "density" calculation has nothing to do with the arguments for why we expect to see million solar mass black holes but not Earth mass black holes. Those arguments are about what kinds of objects can undergo gravitational collapse to black holes, and do not depend on the physically meaningless "density" of the hole once it is formed.

If an amount of matter is uniformly distributed throughout its schwarzschild radius then it is already a black hole fully inside its event horizon. It will of course not remain uniformly distributed, but it is a perfectly valid initial condition

Not if the matter is claimed to be at rest. It is impossible for any distribution of matter to be at rest inside a sphere with a surface area having an areal radius less than 9/8 of the Schwarzschild radius corresponding to its externally measured mass. This is a simple consequence of Buchdahl's Theorem.

If the matter is not at rest but collapsing inward, then, while technically this counts as an "initial condition" (since in a deterministic theory you can call any condition an "initial condition" if you like), calling it that does not strike me as a good use of ordinary language, and trying to describe things that way is very likely to confuse people into thinking that a black hole can be viewed as some kind of static object where the matter just happens to be sitting just inside the Schwarzschild radius. Which it isn't.

Leonard Susskind uses this type of argument in his GR course.

Then that just gives me another reason not to be a fan of Susskind.

 

[Dale]

But, as I've already said several times, this "density" is physically meaningless, and the process is not a process of anything being "compressed". It's gravitational collapse, which is something different.

I am not talking about gravitational collapse. I am talking about the initial conditions prior to the collapse.

Not if the matter is claimed to be at rest. It is impossible for any distribution of matter to be at rest inside a sphere with a surface area having an areal radius less than 9/8 of the Schwarzschild radius corresponding to its externally measured mass.

I am not making any claims about being at rest, just density. However, my understanding of Buchdahl’s theorem is that it places a limit on static configurations, I.e. momentarily at rest is fine it just won’t remain at rest.

likely to confuse people into thinking that a black hole can be viewed as some kind of static object where the matter just happens to be sitting just inside the Schwarzschild radius. Which it isn't.

I agree.

Then that just gives me another reason not to be a fan of Susskind.

That is fine, but I liked the lecture series. It was not pop sci, but a gentle introduction. The point that he made was a valid point. Basically, the point is that for any given density, there is a finite amount of mass that at that density will form a black hole. So the conditions for formation of a black hole are not at all exotic, all you need is a lot of ordinary matter. Thus we are almost guaranteed that they exist since the conditions for their formation are so ordinary.

 

[PeterDonis]

momentarily at rest is fine it just won’t remain at rest.

I don't think this is true either, at least not in any physically reasonable sense.

Mathematically speaking, yes, I think there are solutions that describe a spherically symmetric region of dust with finite extent that starts out with zero surface area, expands to a maximal surface area that could correspond to an areal radius less than 9/8 of the Schwarzschild radius corresponding to its externally measured mass, but still greater than that Schwarzschild radius, is momentarily at rest at that maximal areal radius, and then collapses back to zero radius. But such a solution would have an initial "white hole" singularity as well as a final "black hole" singularity, and is therefore not physically reasonable. (Such a solution would also have a "white hole" past horizon as well as a "black hole" future horizon.)

Also, even mathematically speaking, I don't think there are any valid solutions that have a maximal areal radius that is less than or equal to the Schwarzschild radius corresponding to the externally measured mass. The reason is that such a solution would have to have a single horizon that played the role of both the past and future horizons (since the matter never goes outside the horizon), and that is not possible, because those two horizons must be distinct (for example, on a Kruskal spacetime diagram they are perpendicular to each other--looking at a Kruskal diagram and trying to imagine how the region of matter would look if it never went outside the horizon can also help to see why such a solution is not possible). So if we are talking about the matter occupying a region with surface area less than the horizon area, it is impossible for it to be at rest even momentarily.

the conditions for formation of a black hole are not at all exotic, all you need is a lot of ordinary matter. Thus we are almost guaranteed that they exist since the conditions for their formation are so ordinary.

I agree with this statement as a general statement, but I do not agree with Susskind's way of justifying it.

 

[PeterDonis]

momentarily at rest is fine

Btw, an even simpler way of seeing that even "momentarily at rest" is impossible inside the horizon is to note that, for the matter to be even momentarily at rest, there must be a point on its worldline at which its 4-velocity points in a direction of constant areal radius (this will be the point at which it is momentarily at rest). But there are no such vectors inside the horizon that are timelike, or even null; all vectors pointing in the direction of constant areal radius inside the horizon are spacelike.

 

[Dale]

The reason is that such a solution would have to have a single horizon that played the role of both the past and future horizons (since the matter never goes outside the horizon),

Yes, that’s a good point. Anyway, as I said above, I am not making any claims about the initial velocity. But regardless of the velocity the density is a valid thing to include in the characterization of the initial conditions.

I agree with this statement as a general statement, but I do not agree with Susskind's way of justifying it.

It made sense to me.

 

[PeterDonis]

regardless of the velocity the density is a valid thing to include in the characterization of the initial conditions.

Again, while this is technically true, since in a deterministic system you can call conditions at any time "initial", I don't think referring to the state of dust collapsing inward with a surface area just a bit less than the horizon area as "initial conditions" is a good choice of language. The "initial condition" should be the condition of the original object that started the collapse.

It made sense to me.

I can make sense of it if I interpret him as describing a cloud of dust that is collapsing inward and has a surface area just a bit less than the horizon area for its mass. But for the reasons I have given, I think describing this as an "initial condition" is seriously misleading. Such a cloud will never just occur on its own; it will always be an intermediate state in a process of gravitational collapse from some larger object like a massive star.

 

[sweet springs]

A black hole is vacuum everywhere, outside and inside, so this integral will give zero. If you got M, you did it wrong.

Honestly I could integrate t only outside Schwartzshild sphere. I did not and even now do not know formula of t inside the shere.

 

[PeterDonis]

I could integrate t only outside Schwartzshild sphere.

So what? The region is still vacuum and the integral still gives zero.

 

[sweet springs]

(T^{\mu\nu}+t^{\mu\nu})_{,\nu}=0
I am afraid you refer to T. I am referring t, stress-energy pseudotensor for the gravitational field.

 

[PeterDonis]

I am referring t, stress-energy pseudotensor for the gravitational field.

There is no unique definition for this. Which definition are you using? What reference are you taking it from?

 

[hkyriazi]

I disagree. We don’t know of any natural process which will take an isolated Earth mass and compress it to a density ~13 times the density of atomic nuclei. We do know of natural processes which will take an isolated million solar mass and compress it to the density of water. Therefore we expect to see million solar mass black holes but not Earth mass black holes.

So, do we think there are any black holes (BHs) of mass in between that of the Earth and a million suns, such that a naive calculation of their density, based on their mass and Schwarzschild radius, comes out in between that of a neutron star (10¹⁸ kg/m³ max) and the extremely high, 10³⁰ kg/m³ calculated as required for any Earth mass BH?

 

[PeterDonis]

do we think there are any black holes (BHs) of mass in between that of the Earth and a million suns

Of course. We expect black holes we can observe in our universe now to fall into at least two categories: stellar mass holes massing a few suns to a few tens of suns, formed by gravitational collapse of stars; and supermassive holes, massing millions to billions of suns or more, formed most likely by conglomeration of many smaller holes (or possibly a combination of that and many stars falling into the hole as it grows).

We do not expect earth-mass black holes (or holes of any mass much smaller than the mass of the sun or so) to form by gravitational collapse because the collapse would stop at the white dwarf or neutron star stage and never proceed further. It is possible that earth-mass black holes were formed in the very early universe, due to fluctuations in the density and pressure of matter and energy; we still have a rather sketchy understanding of the constraints on any such process, so it is hard to say whether any significant number of holes much smaller than the mass of the sun might have been formed in this way. My sense is that most cosmologists consider it unlikely, but the question is still open (and cosmologists continue to look for ways of pinning down the possibilities more tightly).

 

[sweet springs]

There is no unique definition for this. Which definition are you using? What reference are you taking it from?

I agree with you that t, a pseudotensor not a tensor, is not unike. I took t_E for my calculation, not t_L-L or others, where E means Einstein's definition and L-L means definition in Landau Lifshitz text. I took these names from Gravitation by Misner, Thorne and Wheeler.

I just want to know right answer to the question:
Where is the rest energy, or mass, of BH ?
(a)All rest energy is within Schwartzshild's sphere.
(b)All rest energy is outside Schwatrtzshild's sphere.
(c)Some are within and others are outside Sphere.
(d)It has no unike defined location.
(e)a catefory-error, silly question!

 

[Boing3000]

Such a cloud will never just occur on its own; it will always be an intermediate state in a process of gravitational collapse from some larger object like a massive star.

What about up-scaling the initial "cloud" to entire Galaxies that are somewhat doomed to cross each others (which is not so unrealistic, I think)
How many of those (no so dense) object are needed to be superposed to "become" a black hole ?
A related question, given the theoretical density of the universe, does it have a Schwartzshild radius (most probably bigger than the observable universe) or is the concept not even correct at such scale ?

 

[PeterDonis]

Where is the rest energy, or mass, of BH ?

In the idealized, maximally extended Schwarzschild spacetime, it's nowhere; the spacetime has zero stress-energy everywhere.

In a more realistic model like the Oppenheimer-Snyder model of gravitational collapse, the region of nonzero stress-energy is mostly in the past, inside the object that ended up collapsing. There is a portion of that region inside the black hole's horizon, but it quickly collapses to zero radius and forms the singularity, so most of the interior of the hole (inside the horizon) is vacuum, and the exterior of the hole once the object has collapsed is also vacuum.

The best way to view it is to consider the "mass" of the hole as a global property of the spacetime geometry, not something that is localized to any particular region. So of your choices, (e) is probably the best.

 

[PeterDonis]

What about up-scaling the initial "cloud" to entire Galaxies that are somewhat doomed to cross each others (which is not so unrealistic, I think)
How many of those (no so dense) object are needed to be superposed to "become" a black hole ?

My answer doesn't change. Galaxies are made up of stars and clouds of gas and dust. If a bunch of galaxies merged to form a superdupermassive black hole, it would be a process of conglomeration of smaller holes (at the very least, the supermassive holes already at the centers of the galaxies) and stars and gas and dust falling in. There is no plausible scenario where galaxies just happen to "superpose" so that a superdupermassive black hole gets created "in an instant" as they all reach just the right positions.

given the theoretical density of the universe, does it have a Schwartzshild radius (most probably bigger than the observable universe) or is the concept not even correct at such scale ?

It's not a matter of scale, it's a matter of spacetime geometry. The concept of "Schwarzschild radius" only applies to the spacetime geometry of an isolated object or system of objects surrounded by vacuum. It does not apply to the universe as a whole since the universe as a whole is not an isolated system surrounded by vacuum.

 

[.Scott]

If an amount of matter is uniformly distributed throughout its schwarzschild radius then it is already a black hole fully inside its event horizon. It will of course not remain uniformly distributed, but it is a perfectly valid initial condition that gives an easy plausibility check.

Is there even such a thing as "evenly distributed" inside the event horizon?

 

[PeterDonis]

Is there even such a thing as "evenly distributed" inside the event horizon?

For an instant, in certain idealized models, yes, there can be. The example that I have had in mind in my previous responses to @Dale is the Oppenheimer-Snyder model of spherically symmetric collapse of dust. At the instant when the outer surface of the dust is just crossing the event horizon, the dust has uniform density and occupies the entire space inside the horizon (note that at this instant, the singularity has not formed and so there is a well-defined notion of "the space inside the horizon" that is finite). However, the dust is collapsing inward and so this "evenly distributed" state is only that way for an instant.

 

[Dale]

Also, “evenly distributed” is inherently frame variant for dynamic scenarios

 

[PeterDonis]

“evenly distributed” is inherently frame variant for dynamic scenarios

Yes, agreed. In post #35 I was implicitly adopting what amounts to FRW coordinates on the dust region.

 

[sweet springs]

The best way to view it is to consider the "mass" of the hole as a global property of the spacetime geometry, not something that is localized to any particular region. So of your choices, (e) is probably the best.

Thanks. I would like this view be in accordance with the view of observers who are far away from BH so whose space time is almost Minkowsy, that rest energy or mass of BH is localized at BH or at the region nearby BH at least.

 

[PeterDonis]

I would like this view be in accordance with the view of observers who are far away from BH so whose space time is almost Minkowsy, that rest energy or mass of BH is localized at BH or at the region nearby BH at least.

Far away observers can certainly take this view, since the spacetime is vacuum in their region so there is no stress-energy anywhere near them. But they should not expect to be able to move close to the BH and find any localized stress-energy anywhere. They won't. Even if they fall into the hole, they won't see anything but vacuum until they hit the singularity.

 

[Boing3000]

There is no plausible scenario where galaxies just happen to "superpose" so that a superdupermassive black hole gets created "in an instant" as they all reach just the right positions.

No, certainly not plausible, but not that far fetched either. Incidentally the wiki article give a lot of referenced of scale. It even bother to compute the Schwarzschild radius for the "observable universe" that is (probably not coincidentally) 13.7 Billion ...quite like the age of the universe (at light speed without inflation).

Anyway some rough computation got me that you'll only need +- 500 identical Milky-way on top of each other, so they "became" a Black Hole (given that there is enough empty space around).
500 it is not that much, given the average local density is quite low, and local curvature should still be quite flat, or am I missing something ? Anyhow I cannot help wondering what would happens if you were inside such an event. I am guessing not much, but you seem to be quite formal that nothing can exist inside a BH.

It's not a matter of scale, it's a matter of spacetime geometry. The concept of "Schwarzschild radius" only applies to the spacetime geometry of an isolated object or system of objects surrounded by vacuum. It does not apply to the universe as a whole since the universe as a whole is not an isolated system surrounded by vacuum.

Got it.
But now I am wondering if you could "unwind" a BH but changing the curvature outside of it. Would the presence of a lot of matter around a BH (I know that one IS far fetched) change the BH far away apparent Schwarzschild radius ?

 

[martinbn]

It even bother to compute the Schwarzschild radius for the "observable universe" that is (probably not coincidentally) 13.7 Billion ...quite like the age of the universe (at light speed without inflation).

The radius of the observable universe is 46billion (if I remember correctly).

 

[Boing3000]

The radius of the observable universe is 46billion (if I remember correctly).

I find the connection with 13.7 quite bizarre. I don't believe in coincidence. I don't even think black-matter has been factored in.
My computation got me: 8.75 * 10^52 kg for a 13.7 Schwarzschild radius black hole

and this page seems to evaluate the mass of the universe to:
2.072 × 10^53 (without dark matter/energy),

But the wiki page (also 1^53) seems to include "dark content".

I know that at one time the observable universe was smaller than that, and it seems to point to the fact that there was no vacuum "outside" of it (it is now un-observable, but kind of still is indirectly). Or is it that the general expansion modify the curvature enough so that even with "vacuum outside" would not induce a BH geometry ?

 

[PeterDonis]

certainly not plausible, but not that far fetched either

I think you need to take a step back and consider carefully before you make such a claim.

some rough computation got me that you'll only need +- 500 identical Milky-way on top of each other, so they "became" a Black Hole (given that there is enough empty space around).

And you think this is not "far fetched"?

Apart from anything else, you are failing to take into account that 500 Milky Ways, each composed of a few hundred billion stars, plus clouds of gas and dust, would have a very complicated dynamics. The idea that they could somehow just end up "all on top of each other" in an instant and form a black hole at that instant is indeed far-fetched.

now I am wondering if you could "unwind" a BH but changing the curvature outside of it

I have no idea what you mean by this.

 

[PeterDonis]

It even bother to compute the Schwarzschild radius for the "observable universe"

Which is meaningless since the observable universe does not have Schwarzschild spacetime geometry. Wikipedia is not a reliable source.

 

[Boing3000]

And you think this is not "far fetched"?

not that far fetched. And I am carefull, minds you.

Apart from anything else, you are failing to take into account that 500 Milky Ways,

No I didn't, the very reason is that it is *I* that put them in the scenario.

each composed of a few hundred billion stars, plus clouds of gas and dust, would have a very complicated dynamics.

That's, of course, irrelevant. Nobody, especially me, said that it is was likely of even plausible, nor that the dynamic would be "simple"

The idea that they could somehow just end up "all on top of each other" in an instant and form a black hole at that instant is indeed far-fetched.

It is, but not that far fetched. The universe is a big place Peter, we happens to live in a Galaxy that is on a collision course with another. 500 is just 2 order of magnitude away from 2. Beside there are denser clusters than ours. And some cluster (500 ?) are bound enough by gravity so that they should survive the tearing appart from expansion.
Besides on a greater scale than galaxies (cluster) the "volumetric density" required is even lower. So the scenario stands, even if the "instant" comes about after half a million years a building...
So does the scenario of post#16 which is after all a thought experiment. Again: the question is: What does GR predicts for what would happens inside that volume of space (surrounded by as much deep vacuums you need)

I have no idea what you mean by this.

OK, let me explain (beware, that scenario is really far fetched).
1) We found an Earth mass black hole (~1 cm across)
2) We somewhat managed to drop synchronously from from orbits 2 half sphere of great thickness and strength so they meet exactly around the BH (let's say the initial interior radius is (1 meter, 10 meter, 1 kilometer ?). Curvature is strong, but will it systematically destroy the sphere (given it is still only 1G of acceleration somehow)
3) On top of the sphere, we pack as much mass as possible (taking care of momentum so the sphere never "touch" the even horizon) without breaking the sphere.

The question is: Does that added curvature outside the hole, change the radius of the horizon ?(1)

The really really really far fetched thought experiment would be to scale up the experiment to a HUGE proto black hole gaz cloud, kept from collapsing by "external(at outer surface)" mass curvature, that could be suddenly moved outward, creating enough vacuum so the BH form.
What if the mass is suddenly re-set inward, would that affect the BH formation ?(related to (1))

Are such simulation even possible ?

 

[PeterDonis]

not that far fetched

IMO you have not justified this claim at all. But it's a subjective claim, and evidently your standards for what counts as "far-fetched" are different from mine.

What does GR predicts for what would happens inside that volume of space

You haven't specified the scenario precisely enough to tell. You say the dynamics are irrelevant, but unless you know the dynamics you don't know what GR predicts. There is certainly no idealized, highly symmetric model like Schwarzschild spacetime that will let you extract qualitative answers for this case without having to do detailed computations of the dynamics.

Remember that, in the original comments of mine that appear to have spawned this sub-thread, I wasn't saying that a black hole could not form by a process like this. I was only saying that you can't just compute the "density" (using the physically meaningless formula described in the OP of this thread) and expect that to give you a simple rule for exactly when the black hole forms. It doesn't work that way; the dynamics is complicated, whether you want to think about them or not, and that means the criteria for when a black hole is formed are also complicated.

Does that added curvature outside the hole, change the radius of the horizon ?

You haven't specified the scenario precisely enough to tell (because it's possible that the sphere could be close enough to the hole that it would be forced to fall in, increasing the hole's mass). But here is a general statement that might help: if you have a static (meaning it won't collapse), spherically symmetric shell of matter with vacuum inside, the shell has no effect on spacetime curvature in the region inside. That means that whatever is inside is the sole determinant of the curvature inside.

 

[Boing3000]

You haven't specified the scenario precisely enough to tell. You say the dynamics are irrelevant, but unless you know the dynamics you don't know what GR predicts.There is certainly no idealized, highly symmetric model like Schwarzschild spacetime that will let you extract qualitative answers for this case without having to do detailed computations of the dynamics.

Fair enough. I could add that all galaxies are parallel, that half the galaxies are rotating one way, and they come equally from all direction. The goeal is to have an average momentum(and angular momentum) of 0.
Another scenario would be a kugelblitz has described here. The dynamic of interest for me, is what happens INSIDE the BH. I think GR can describe it, but I don't think that any dramatic change should be experienced inside the BH. Well, not faster than light anyway.

I was only saying that you can't just compute the "density" (using the physically meaningless formula described in the OP of this thread) and expect that to give you a simple rule for exactly when the black hole forms. It doesn't work that way; the dynamics is complicated, whether you want to think about them or not, and that means the criteria for when a black hole is formed are also complicated.

Indeed, and I have another scenario in mind. Maybe I'll start another thread with it.

You haven't specified the scenario precisely enough to tell (because it's possible that the sphere could be close enough to the hole that it would be forced to fall in, increasing the hole's mass).

Well, I cannot be more precise. I give some diameter of choices (not too far fetched), I don't see what I can add to that (maybe the Earth BH is non-rotating and uncharged)

But here is a general statement that might help: if you have a static (meaning it won't collapse), spherically symmetric shell of matter with vacuum inside, the shell has no effect on spacetime curvature in the region inside. That means that whatever is inside is the sole determinant of the curvature inside.

But the if is known to be false. I though that Newton shell theorem would not apply anyway (due to strong enough curvature).
I get that global(possibly to infinity ?) geometry is important for BH formation, and that why the universe is not a BH (there is no vacuum outside the universe).

It just get me to wonder if a local measuring device on the interior of the sphere would notice a change in the horizon local radius, when more and more mass was added on the outer shell. I am going to assume no change.

Also, do you have any opinion on the coincidence between the "physically meaningless formula" that nonetheless happens to give 13.7 Bly radius for a pseudo BH with the mass of the observable universe ?

 

[PeterDonis]

the if is known to be false.

It is? Weren't you describing the assembly, from two half-shells, of a spherical shell of matter with vacuum inside? (Remember that a black hole is vacuum.)

I though that Newton shell theorem would not apply anyway

You are wrong. The shell theorem, as I stated it, holds in GR.

a local measuring device on the interior of the sphere would notice a change in the horizon local radius,

There is no such thing as "horizon local radius". The radius of the horizon is a global, not a local, property. There is no way to locally measure where the horizon is or what its radius (more precisely, its area) is.

do you have any opinion on the coincidence between the "physically meaningless formula" that nonetheless happens to give 13.7 Bly radius for a pseudo BH with the mass of the observable universe ?

I already gave my opinion: it's meaningless.

 

[martinbn]

Also, do you have any opinion on the coincidence between the "physically meaningless formula" that nonetheless happens to give 13.7 Bly radius for a pseudo BH with the mass of the observable universe ?

As already pointed out it is meaningless, but what exactly is the coincidence? The radius of the observable universe is a lot more than 13.7bly.

 

[Boing3000]

(Remember that a black hole is vacuum.)

Ho, I thought you were jesting there. OK, you've made up quite a new definition of vacuum (we both know its not, there is at least a singularity, and there is mass anyway). You got me there.

You are wrong. The shell theorem, as I stated it, holds in GR.

Then I'll start the new thread, a new scenario is coming

There is no such thing as "horizon local radius". The radius of the horizon is a global, not a local, property. There is no way to locally measure where the horizon is or what its radius (more precisely, its area) is.

Not as such, but we surely can measure the change of the horizon by shooting a laser and seeing if it hit a detector somewhere or elsewhere (or no more).

I already gave my opinion: it's meaningless.

As allready pointed out it is meaningless, but what exactly is the coincidence? The radius of the observable universe is a lot more than 13.7bly.

OK fine. That's bizarre. We just can compute that all the particle of the universe seems to be at the center of a singularity 13.7 by old. And that's actually confirmed somehow by observation.

I think I heard once Susskind say something like that (kind of: that's like if we are inside a BH) but right now, I cannot find the lecture...