# 3-dimensional implications of a black hole

wetwonder
I am loving this forum :)

I am troubled by the conventional image of space being inverted by a black hole - if that's the correct way to phrase it. But I'd like to take a step back and use a model to explain.

We observe an enclosed room, shaped like a cube, with 1,000 cubic feet of space (10x10x10).

Then in this room we place, in the center of the floor, a cube shaped sponge, which is 125 cubic feet (5x5x5).

So the space in the room is now less than 1,000 cubic feet. It would be 1,000 minus 125 = 875. Yet, we still have to account for the space within the cube shaped sponge. For the sake of discussion, the cube shaped sponge here has 25 cubic feet of space within it. So add 25 to 875, and the space in the room is now 900 square feet. The matter takes up 100 cubic feet within the cube shaped sponge.

Now we add matter to the sponge until it's infinitely dense. There is now no more space with the sponge. That means the space within the room drops to 875 cubic feet, and the infinitely dense matter within the cube space sponge takes up 125 cubic feet.

Thus, having no space within the sponge - the question is "would this now be considered a hole in space?" A hole in space must take up 3-dimensional space. It's seems counter-intuitive to how a layman would describe a hole. A conventional hole is a hole in matter, which would increase space. But a hole in space would to the contrary, increase matter and decrease space.

Is this correct? The initial aspect of the infinitely dense matter would be a "hole in space." Is this different than a "black hole in space," where I envisioned the inversion of space due to space being unable to manage the effects of infinite density in its normal state (as we normally see it)? Or is a black whole still using up space (as described above) to the extent of its dimensions as an object of matter?

Thanks, Dave

Mentor
The volume of the room is always 1000m^3, no matter how much matter you put into - unless you want to transform your sponge into a real black hole.
Edit: Feet? Whatever. 1000 cubic feet then.

"A hole in space" is an area where the conventional volume concept does not work. For example, in a black hole with a Schwarzschild radius of 3km, it is meaningless to talk about "points 2km away from the center". You cannot put a ruler there and measure a length.

wetwonder
Volume would always contain space and matter.
The 1,000 cubic feet I speak of is a room absent of matter, so the space (matterless) is 1,000 cubic feet. When you introduce matter into the room, then there would be less space - is that not correct? Where the matter has space curve around it, the matter displaces space.

Would not a hole in space (the infinitely dense sponge), within that room, displace the space totally within the coordinate 3 dimensional shape of the hole?

(The "black" in black hole, to me, just describes a condition of the hole that has the capacity to effect it's surrounds in predicted ways eg. precluding terminal velocities, etc.

But here above, I'm talking about the moment before the hole goes "black." For the sake of distinguishing it, let's say the we add matter to the sponge to where it gets to infinite density minus 1 (the moment before "black" effect)..)

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Mentor
When you introduce matter into the room, then there would be less space - is that not correct? Where the matter has space curve around it, the matter displaces space.
No. Space is there, even with a sponge inside.

(the infinitely dense sponge)
That does not exist. If you keep adding mass to a sponge, it will distort space around it (which makes the definition of "volume" a bit tricky), until it finally becomes a black hole - if you keep adding mass, you just increase the black hole size. But that does not mean that matter would somehow "remove" space. It just removes the possibility to assign a meaningful volume to the room.

(The "black" in black hole, to me, just describes a condition of the hole that has the capacity to effect it's surrounds in predicted ways eg. precluding terminal velocities, etc.
It is called "black" because no light (and nothing else) can escape from the inside.

wetwonder
Hum OK. Thanks very much. It just seems like, if you make a hole in the ground, the difference is that there is an absence of ground relative to the size of the hole. So if you made a whole in space, there would be an absence of space relative to the size of the hole. Maybe I'm being too fundamental. Any matter should make holes in space (of course the spaces within the matter relative to density would not be a hole or part of the hole). But holes should be all around us. They just don't meet the criteria of black holes.

wetwonder
Wait, you're saying the same amount of space is there, it's just altered by being warped by the matter. Is that right?

Gold Member
A black hole is 'infinitely' dense only at the singularity, which is a zero volume point containing mass. Most scientists believe the putative singularity merely represent the point where the equations cease to yield a meaningful answer, not that there are actual regions of space that contain matter, but, not volume.

SHISHKABOB
black holes aren't "holes" in the sense that a hole in the ground is a hole

it's called a hole because whatever goes in never comes back out. Also because it's unknown what's inside a black hole, think "down the rabbit hole" from Alice in Wonderland.

wetwonder
Yes thanks. Those are all great and I understand it better now.

I wasn't trying to work backwards from what a black hole was to how it is formed. I was just thinking intuitively. Just made up in my head from scratch. (One of my law professors would call this a thought experiment.)

Eg., if you have a baseball, the denser it is the less space is within it. If you made it 100% dense - bear me out, this is only a thought experiment - then it would intuitively be a hole in space relative to the dimensions of the ball. This way of looking at it here stands on its own, just an experiment in my head. A hole in the ground could be viewed as negative, a hole in space in this little experiment can be viewed as positive.

I see you can't have a infinitely dense baseball, and the measure is when it becomes meaningless, and it's not important to have no volume - all real physics. I was just thinking about it; the questions that came to mind.

Mentor
Hum OK. Thanks very much. It just seems like, if you make a hole in the ground, the difference is that there is an absence of ground relative to the size of the hole. So if you made a whole in space, there would be an absence of space relative to the size of the hole.
No.

There is no "100% dense". There is no meaningful way to give a dimensionless density at all.

ImaLooser
Eg., if you have a baseball, the denser it is the less space is within it. If you made it 100% dense - bear me out, this is only a thought experiment - then it would intuitively be a hole in space relative to the dimensions of the ball.

Aha. Such a thing is possible. The average atom here on Earth is about 99.99999% empty space. "Solid" mater is really just excitations of the electromagnetic field.

Under intense gravity the empty space is indeed squeezed out. One then gets matter which contains no empty space whatsoever. This happens in the cores of neutron stars, which are not quite dense enough to become a black hole. The central core is about ten times as dense as an atomic nucleus. So yes, you could say that was a hole in empty space because there is no emptiness.

If the matter gets much denser than that then the matter collapses entirely. Nothing at all can get out and no one knows what goes on in there. Our ideas of time and space lose all meaning. It's a "hole" because it is possible to fall into it, and "black" because no energy can get out.

wetwonder
Nice, thanks again Iam, Dave

Mentor
@ImaLooser: No, that does not work.

The average atom here on Earth is about 99.99999% empty space.
If you consider electrons as point-like with no volume, you have to do the same for the components of nucleons, and you get 100% empty space.
If you consider the wave functions as "filled with electrons", you get 0% empty space (one can argue that gas is below that value, but at least in solids it is true).
Considering a proton wave function as "not empty space" and an electron wave function as "empty space" is inconsistent.

One then gets matter which contains no empty space whatsoever.
Neutrons stars are filled with neutron wave functions, similar to atoms with electron wave functions. There is no qualitative difference, just a quantitative (more neutrons per volume and neutrons are heavier than electrons).

wetwonder
so irrespective of how you look at space relative to the neutron or electron -

is the tipping point for mass to create a black whole, the increase in its density, or the decrease in the space within the mass? If it was the ladder, than that would be a constant right? - cause the makeup of space can't be variable like the matter/density relationship, dependent on the type of matter.

Mentor
It is mass per radius, so the required density depends on the total mass - if you compress something of the mass of sun to <=3km radius, it will become a black hole. If you compress something with twice the mass to <=6km radius (8 times the original volume), it will become a black hole.

SHISHKABOB
adding mass to something doesn't decrease the amount of space in something. A cubic meter of lead takes up a cubic meter of space just like a cubic meter of air takes up a cubic meter of space.

wetwonder
If you were doing an EVM outside the space shuttle, and tethered to the exterior of the shuttle was a cubic meter of lead and a cubic meter of a sea sponge, are you saying the cubic meter of lead wouldn't have less space within it than the sea sponge? Or if it was a cubic meter of lead vs. a cubic meter of balsa wood that the lead wouldn't have less space within it?

wetwonder
SHISHKABOB
If you were doing an EVM outside the space shuttle, and tethered to the exterior of the shuttle was a cubic meter of lead and a cubic meter of a sea sponge, are you saying the cubic meter of lead wouldn't have less space within it than the sea sponge? Or if it was a cubic meter of lead vs. a cubic meter of balsa wood that the lead wouldn't have less space within it?

do you mean "empty space"?

wetwonder
I'm coming from the premise that where there is matter, there is not space, and where there is space there is not matter. That's how I was approaching this. I wasn't thinking of an imaginary sense of "volume."

Staff Emeritus
I'm coming from the premise that where there is matter, there is not space, and where there is space there is not matter. That's how I was approaching this. I wasn't thinking of an imaginary sense of "volume."

The sea sponge is filled with empty holes that have nothing but vacuum, while the lead is one continuous solid object. You could add air or liquid into the sponge, and this may or may not mean it now takes up more space than before depending on how you choose to look at it.

wetwonder
I don't see how, but the sea sponge is a bad example because there are too many preconceptions about its structure. So put the sea sponge aside and use a cubic foot of solid wood instead.

If the cubic foot of solid wood and cubit foot of lead are both tethered off the space shuttle, there would be more space within the dimensions of the wood than the lead.

If the lead and the wood were to run into each other at a high speed, the wood will show a perceptible dent (without any splintering off in this eg.) - there is still the same amount of wood, but it's been compressed by its mass displacing space inside. The lead may have a tiny dent, so it displaced much less space then the wood, partly because there was less space available to displace.

Mentor
I'm coming from the premise that where there is matter, there is not space, and where there is space there is not matter.
What you describe is called "vacuum". If you call vacuum "space" (which has a specific and different meaning), you are confusing others, so please do not do that.

I wasn't thinking of an imaginary sense of "volume."
But everyone else did, probably.

SHISHKABOB
"space" is, as I understand it, a way to conceptualize the relationships between objects

in other words, it's not really a "something", instead it's just a very intuitive way to understand reality

I think you're using the word "space" and "volume" interchangeably

Staff Emeritus
If the cubic foot of solid wood and cubit foot of lead are both tethered off the space shuttle, there would be more space within the dimensions of the wood than the lead.

This depends HIGHLY on what you define "space" and "vacuum" to be. If you think the space between electrons and the nucleus is empty, and that fundamental particles are point-like, then the vast majority space that matter occupies is indeed empty. However, if you view particles as occupying the portion of space where their wavefunction says they are most likely to be found, and you view forces between particles as "something", then matter is not mostly empty space. It gets even more complicated if we delve into QED and QCD and bring virtual particles and such into it.

If the lead and the wood were to run into each other at a high speed, the wood will show a perceptible dent (without any splintering off in this eg.) - there is still the same amount of wood, but it's been compressed by its mass displacing space inside. The lead may have a tiny dent, so it displaced much less space then the wood, partly because there was less space available to displace.

I think this goes back to the sponge issue. Wood is not fully solid. It has water and gasses inside it and is made up of complex molecules. If you really want to compare to objects, let's compare Aluminum and Lead. Aluminum has an atomic radius of 143 picometers, while lead is 175 pm. Yet lead has much more mass even though it is larger, giving it a much higher density. You could say that there is less empty space inside lead if you want to. But let me ask you this. Where is a particles "surface"? How can we say how big it is?

wetwonder
Nice good example, aluminum and lead. (I'll be more careful also with my use of space and volume.)

There must actually be space all over the place inside a mass, being warped by all the matter in there and making gravities pulling every which way relative to the relationship of the matter - otherwise there would be no structure, no order. And one must have more space inside its dimensions than the other - differentiating the characteristic/structures of the two.

Staff Emeritus
Nice good example, aluminum and lead. (I'll be more careful also with my use of space and volume.)

There must actually be space all over the place inside a mass, being warped by all the matter in there and making gravities pulling every which way relative to the relationship of the matter - otherwise there would be no structure, no order. And one must have more space inside its dimensions than the other - differentiating the characteristic/structures of the two.

The structure of all objects on our scale is dominated by electromagnetic interactions, not gravity. Molecules are held together by balancing the attraction and repulsion of their atoms. Only when you get to very large objects such as moons, planets, etc does gravity start to play a dominant role.

I can't say much on there being more spacetime inside an object, as I don't know.

ImaLooser
I'm coming from the premise that where there is matter, there is not space, and where there is space there is not matter. That's how I was approaching this. I wasn't thinking of an imaginary sense of "volume."

Your concept is perfectly OK, but that is not the way physicists think of it. They generally think of space as "existing" and matter passing through space having no effect on space.

Either way of looking at it makes sense. They way I see it, either way works equally well, so you may as well use the same definition everyone else does in order to avoid misunderstandings.

I have a policy of refusing to argue about definitions. I'll just use whatever definition the other guy wants. (Political discussions in particular often devolve into endless arguments about definitions. Since definitions are arbitrary, to me this seems pointless.)

Some is sure to point out that according to Einstein matter and space do affect one another, but this is so complicated and hard to work with that physicists avoid using this theory. Instead they stick with Isaac Newton's much simpler ideas, which are almost always accurate enough.