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Hollow spherical blackhole thought experiment

  1. Jun 18, 2006 #1
    I have a thought experiment for anyone interested. All replies welcome:


    Imagine if you will, a large spherical body e.g. a moon, about the surface of which are placed many large thermonuclear devices. Deep inside the moon sits an intrepid/foolish experimental physicist. When the the devices are triggered, the surface of the moon is crushed so quickly and uniformly and with such force as to create a spherical blackhole. However the critical density is reach first, only by the 'crust' of the moon. meaning the fool/heroic physicist is, for an instance at least, completely surrounded by blackhole.

    It is my belief that this puts him beyond our universe. And we, beyond his. My first question is, if the blackhole then 'evaporated', where/when would our fool/hero and his/her moon's interior reappear, if at all?

    Although this is all highly improbable to the point of absurdity, its worth noting, that in theory the fool/hero would not be crushed by the gravitational field of the spherical blackhole surrounding him (do the vector analysis if you like), unlike anyone unfortunate enough to fall through a wormhole.

    Thoughts anyone?
     
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  3. Jun 18, 2006 #2
    I would imagine that the crust wouldn't form a black hole (no matter how powerful the nukes) because it would be 'easier' for the crust to force itself down into the Moon than be crushed into a black hole, in that the Moon's rock would not be able to apply enough pressure to make a black hole.

    It's an interesting notion though, being completel surrounded by a black hole without actually being torn apart. It is probably prohited by Penrose's 'Cosmic Censorship Hypothesis' because if you were in a spherical shell of black hole material (whatever that might be) you'd be able to see the material since there'd be no horizon between you and it.
     
  4. Jun 18, 2006 #3
    Sure enough this is almost certainly true. So I guess my second question is, cxan anyone think of a practical, or at least theretically possible way to produce this scenario?

    No, I think you wouldn't be able to 'see' the event horizon, as the same oneway effect of light that comes into contact with the EH would apply, regardless of it weird geometic nature. As far as I can see. Cheers for the response though. Keep them coming :cool:
     
  5. Jun 19, 2006 #4
    I can't get this to work, how could you create a "hollow" black hole? As soon as you remove sufficient matter from a given area you no longer have the required density to maintain a black hole. The black hole must start by having a sufficiently dense core to draw the matter in to begin the collapse.
     
  6. Jun 19, 2006 #5

    JesseM

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    I don't think an oddly-shaped black hole would be possible--the no-hair theorem says that no matter what the shape of the original collapsing object, all black holes will be identical from the outside except for their mass, charge, and angular momentum (and the size of a black hole depends on its mass, so you can't have two black holes which are identical in these three respects but differ in size because one was formed from a large hollow shell while the other was formed from a more compact object).

    As for what happens to someone who falls inside a black hole that later evaporates, see this answer to an FAQ to sci.physics on black holes:
     
    Last edited: Jun 19, 2006
  7. Jun 19, 2006 #6
    Any such theoretical method of building such a thing would still be “highly improbable to the point of absurdity” as you said in OP. But it might be practical to think of such a construction for the purpose of considering the potential reality of something we can never see - that is looking behind an event horizon. Since no one else has seen behind that horizon, no one can be said to know what is correct.

    Since you have given FP (the Foolish Physicist) extra-natural powers lets allow him to clean up a few details from his center position of this sphere by doing even more of the impossible. Since he needs much more mass than the moon; lets allow him to simply place a black hole some distance R from himself. Although not inside this blackhole, to avoid being pulled immediately into it FP also places an identical blackhole on his opposite side. With the gravity vectors canceling he remains weightless in space and unharmed between them. In like manner he keeps adding identical blackholes , always keeping his lab weightless in the center, but increasing the total mass of all the blackholes added to the sphere structure radius R until it has the mass of a super-blackhole of radius R.

    Now externally we can only see one large black hole – with no hope of “seeing” inside to prove what it looks like in there. But assuming FP can hold this structure together for some time. How would his reference frame in this type of “center” compare to the reference frame of a distant deep space vacuum (roughly equivalent to our own)?
    Obviously the Mass density would not be the same as that in the real blackholes on the surface of the sphere but it would have some value significantly greater than a vacuum.
    What would be the comparative rate of time be verses the stopped time of the small blackhole horizons or the vacuum outside?
    How about the measure of distance? Backwards? Imaginary?
    How would these change as FP’s lab is moved away from the center by a fourth or half of R?
     
  8. Jun 19, 2006 #7

    JesseM

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    Perhaps not, but you can say what would be correct according to the theory of general relativity.
    If he is within a shell of blackholes which itself has enough mass so that each of them lie within the event horizon of a super-black hole, then according to GR it should be inevitable that they will all fall together and form a common singularity, and that the scientist too must be crushed by this singularity in a finite time.
    He can't hold the black holes apart, if that's what you mean. Not according to GR anyway.
    The no-hair theorem says that as long as two black holes have the same mass, charge, and angular momentum, they must have the same size. So this super black hole originally formed from a shell of smaller black holes could not be any larger than a regular black hole formed from a star with the same mass as the total mass of the small black holes in the shell, meaning that its average mass density would not be any different either.
     
  9. Jun 19, 2006 #8
    Well of course he can with absurd extra-natural powers – obviously the OP is speculating on a Black Hole with no Singularity.
    All I did was set up his scenario a little clearer.
    If you have no speculation on what that may mean within the unseen boundary of the horizon that’s fine if you have no comment.
    But what is the point of just telling the OP the idea doesn’t fit your favorite theory or scientist’s ideas so don’t think about that any more?

    Nether GR QM or “no-hair theorem” have a conclusive answer to define singularity as the infinity problem at the center remains. Their resolutions are just a little less speculative than this one.
     
  10. Jun 19, 2006 #9

    JesseM

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    Sure, but I don't think the OP was supposing any extra-natural powers--I think the poster just didn't realize that the idea of a black hole shaped like a hollow shell (formed by compressing matter into a shell of huge density) would fundamentally violate the laws of physics as we know them.
    I think most physicists would say that even though GR is going to give bad predictions at the singularity, its predictions can probably be trusted far from the singularity where you're not dealing with Planck-scale densities and energies. So based on this, my guess is that the no-hair theorem is unlikely to be overturned, at least not at macroscopic scales (micro-black holes whose mass is close to the Planck mass might be a different story).
     
  11. Jun 19, 2006 #10

    pervect

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    To do this with only a moon, you'd need a very tiny physicist.

    For an object the mass of the Earth's moon, for instance (pretty large as far as moons go), the Schwarzschild radius is about 100 microns.

    So we'd have to compress the Earth's moon into a sphere of about 100 microns radius to turn it into a black hole, while somehow leaving a tiny space at the center for the physicist (who would have to be much smaller than 100 microns for this to work).


    I don't think there's really any great mystery about what's going to happen to the (tiny) physicist though. Assuming that he's inside an object made out of normal matter, the walls of whatever it is that is keeping him from being crushed will fail. It takes "exotic matter" to have a pressure greater than c^2 times the density, and only exotic matter could exert enough pressure to protect the physicist.

    I think this is the main point the OP is missing, that there is a limit to the strength of non-exotic matter.

    The rest is a matter of timing and defintions. The fate of the physicist is known (he will be crushed). One gets into arguments about "apparent horizons" vs "absolute horizons". Both of these defintions of horizons (the bounday of the black hole) have counterintiutive poperties when their evolution with time is studied.

    "apparent horizons" can shift instantaenously, and are observer dependent. "Absolute" horizons are the same in all reference frames (observer independent), but are not causal. See Kip Thorne's book "Black Holes & Time Warps", pg 416, for more details.

    Anyway, depending on the details of the defintions of the boundary of the black hole (i.e. the location of the horizon) one might be able to claim that the physicist was "inside a black hole" a bit before he was crushed. However, that isn't particularly odd, anyone can do that by jumping into a normal black hole. They will survive for a time before they die at the singularity.
     
  12. Jun 19, 2006 #11
    Nice progression

    Great reply pervect!

    So if we want our FP to survive, how big do you say the moon/planet/body should be?

    And if all you wanted to do was envelope a 1 meter wide probe, how big does the body need to be?

    Not quite so. Imagine you are inside the sphere of blackhole. Just as the net force felt by a charged particle within a charged sphere is zero, the net gravitational effect of the blackhole, as long as it is perfectly spherical (or cylindrical for that matter), would be zero. Like I say, do the vector analysis
     
  13. Jun 19, 2006 #12
    Nice imagery. My question was though, supposing the shell evaporated before it collapsed, however... And now its gets interesting although there is reason for the blackhole shell to collapse, as seen from 'outside', is there equal reasoning from the inside?

    If you're inside, everything ~X meters away from you is event horizon, so why would physics be working on the other side? How deep would the shell be? Thin enough to evaporate? or as deep as should be expected due to the history perceived by our FP? Why? The time line has been severed. Thick enough not to evaporate and collapse in on our poor FP? On what grounds? The deciding factors on FP's survival don't exist in FP's universe anymore. I believe this is a paradox. I'd like to call it Teare's, unless someone can tell me why its not valid, or not news. :smile:

    Cheers for the replies, and keep them coming.
     
  14. Jun 19, 2006 #13
    Perhaps I am wrong here, but I thought that the centered singularity of a black hole is the source of the extreme gravitational field. As such, how would it even be possible to create a "void" within the center of an infinitesimally small singularity?
    On the other hand(just speculating), what would stop such a singularity from forming a "bubble"?
     
  15. Jun 19, 2006 #14

    Another nice reply. However, the bubble is not being created within the singularity, the blackhole is being created around the bubble.
     
  16. Jun 19, 2006 #15

    pervect

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    The Schwarzschild radius is 2GM/c^2.

    So the Schwarzschild radius of Jupiter, for instance, would be 2.8 meters. Thus if you could compress jupiter into a hollow sphere with a circumference of less than 2*Pi*2.8 meters, it would be a black hole, leaving you enough room inside for a probe or physicist.

    I am not saying that the force in the center would be non-zero if you had a hollow sphere. What I am saying that there is no way to keep the hollow sphere from collapsing under its own weight.

    For instance, if you hollowed out a sphere inside the center of the Earth, there would be no gravity in the hollowed out region, but it would take an extremely strong shell to keep that hollowed out cavity from collapsing.

    To be specific

    http://hypertextbook.com/facts/1999/PavelKhazron.shtml

    puts the pressure at the center of the Earth as about 3 million bars (i.e 3 million times the standard atmospheric pressure). So a sphere that could hold the hollowed out region from being smashed close at the center of the Earth would have to be able to support 3 million atmospheres.

    You are perhaps thinking "But there is no gravitational force on the inside of the sphere". This is correct, but it doesn't explain what supports all the weight on top of the hollow sphere.

    Pressure IS required to support the top part of the sphere, and that pressure is communicated downwards - though the gravity at the center of the Earth becomes zero, the pressure does NOT become zero.

    There is no even theoretically possible material of normal (non-exotic) matter that can stop a black hole from collapsing all the way to a singularity once it has been compressed enough to form a black hole.
     
  17. Jun 20, 2006 #16
    You're totally right that the pressure would be phenomenal, and in real life situations, it already looks like its practically impossible to even get a probe into the 'safe place' in the centre of, say, Jupiter (Cheers for giving us some scale).

    However this is a thought experiment, and we don't have to actually make the thing, just prove its possible in theory.

    So our FP would gets squished by the pressure of the body. However 'all information' is not destroyed by such forces, even within Jupiter. In theory a probe could be put in the situation where it was completely surrounded by, but not actually touching, event horizon. In which case, what happens next?...

    Like I say, whether or not the event horizon evaporates depends on information that does not exist in*the probe's/FP's*universe/space time continuum. Even if the event horizon simply collapses in on poor FP, at what speed would it do this? Again this is dependent on information that does not exist in FP's universe.
     
  18. Jun 20, 2006 #17

    pervect

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    After the physicist is crushed, the collapse process continues. No known force is strong enough to stop it. The forces attempting to resist collapse are fierce - at this point, matter will be in the form of neutron degenerate matter, i.e. neutronium. However, even these fantastically large nuclear forces aren't large enough to prevent collapse.

    Detailed calculations are tricky, but one can look at calculations of simple cases, like a uniform star of constant density, for insight. One can see that in a hypothetical static spherical mass of constant density, above a certain critical radius, the pressure at the center becomes not only large, but infinite.

    http://scienceworld.wolfram.com/physics/SchwarzschildBlackHoleConstantDensity.html

    IIRC this infinite presssure occurs just when the spherical mass becomes a black hole. The conclusion is that such a static spherical star does not exist - the star must collapse under its own weight.

    In a simple spherically symmetric collapse, the physicist becomes part of the central singularity. First the cavity collapses, then you have a spherically symmetrical (but not static) mass that implodes further. Nothing in classical physics can halt the collapse - it proceeds to a mathematical point.

    This is according to classical GR. Most theories of quantum gravity suggest that the mass of the black hole does not collapse to a mathematical point (as classical GR predicts), but probably has some Planck-scale size.

    There is still some room for argument about the details of what happens even in classical GR for realistic (i.e. non-symmetrical) collapse. Rotating collapse is especially problematical, and is still being studied. However, various singularity theorems show that any black hole must have at least one singularity at its center.

    http://en.wikipedia.org/wiki/Penrose-Hawking_singularity_theorems
     
    Last edited: Jun 20, 2006
  19. Jun 20, 2006 #18
    You're still not quite getting my point. From 'outside' the blackhole, yes you're right on all accounts, but that's not my issue.

    From inside...

    If your are surrounded by event horrizon, the depth of the event horizon doesnot exist in your time or space or universe for that matter, only the radious of the event horizon, from the centre of the cavity. From 'inside' the 'event horizon shell', your previous 'outside', doesnot exist. There is no crushing mass beyond. None. The event horizon, is just that. its is the boundry of your universe. And as your universe is not yet crushed out of all existance, why should it be? Why shouldn't the event horizon colapse outwards, evaporate, vanish in a puff of logic etc... There is no beyond. Or thats how I see it. And you've not convinced me otherwise yet.

    From 'outside', there is no paradox. It colapses and become a black hole like any other, very quickly. So its easy to say, the FP is crushed, but equally, FP no longer exists to be crushed. But from the perspective of the FP, there is no reason for the event horizon to act in any perticular way. e.g. How fast should it collapse? You can't go by what's 'outside', because outside doesn't exist. Do you see my point? The logical asymatry comes from being able to measure proerties of a blackhole from outside (radious, mass, charge...) but from inside a spherical shell of event horizon, none of these measurements can be made, or even implied.
     
    Last edited: Jun 20, 2006
  20. Jun 20, 2006 #19

    JesseM

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    But the event horizon must contain the matter that was compressed into a black hole, that's not "beyond the boundary of your universe" if you're inside. And inside the event horizon, you can still use the same laws of general relativity to predict how this matter will behave--if you compressed a hollow shell into a black hole as you suggested, general relativity says the shell must collapse inwards until it has all gathered at a single point, the singularity.
     
  21. Jun 20, 2006 #20
    Why? It is not linked to you through time or space. Nor can any information pass through it to you. But nor (and this is the crux) can you imply any properties beyond it, through observation. Why should your past influence it? Time is no longer shared by FP and the that which is beyond the shell.


    "still" is the give away. There is no still, beyond the event horizon. There is continuity in the usual sense from outside a 'normal' blackhole, because the influence of the blackhole on an observer's universe gives away properties, such as mass. These properties give that which is contained within the singularity a continuous implied history to an external observer. Not so if you're in the shell. I realise this is very much bordering on philosophy, but dismissing it as such would render most of Relativity beyond consideration.

    It is my belief, though I could easily be very wrong, that the event horizon would have to vanish, as otherwise it would be paradoxical. The FP must then reemerge into a universe, but not the one he was in before, as in that one, he was crushed.

    Thoughts...?
     
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