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3-dimensional implications of a black hole

  1. Sep 19, 2012 #1
    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
     
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  3. Sep 19, 2012 #2

    mfb

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    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.
     
  4. Sep 19, 2012 #3
    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)..)
     
    Last edited: Sep 19, 2012
  5. Sep 19, 2012 #4

    mfb

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    No. Space is there, even with a sponge inside.

    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.

    It is called "black" because no light (and nothing else) can escape from the inside.
     
  6. Sep 19, 2012 #5
    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.
     
  7. Sep 19, 2012 #6
    Wait, you're saying the same amount of space is there, it's just altered by being warped by the matter. Is that right?
     
  8. Sep 19, 2012 #7

    Chronos

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    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.
     
  9. Sep 19, 2012 #8
    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.
     
  10. Sep 19, 2012 #9
    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.
     
  11. Sep 19, 2012 #10

    mfb

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    No.

    There is no "100% dense". There is no meaningful way to give a dimensionless density at all.
     
  12. Sep 19, 2012 #11
    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.
     
  13. Sep 19, 2012 #12
    Nice, thx again Iam, Dave
     
  14. Sep 20, 2012 #13

    mfb

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    @ImaLooser: No, that does not work.

    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.

    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).
     
  15. Sep 20, 2012 #14
    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.
     
  16. Sep 20, 2012 #15

    mfb

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    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.
     
  17. Sep 20, 2012 #16
    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.
     
  18. Sep 20, 2012 #17
    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?
     
  19. Sep 20, 2012 #18
  20. Sep 20, 2012 #19
    do you mean "empty space"?
     
  21. Sep 20, 2012 #20
    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."
     
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