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Question about black holes

  1. Sep 21, 2007 #1
    Hi,

    I have a question about black holes that has to do with their evaporation. What is predicted to happen once a black hole evaporates enough matter that its Schwarzchild Radius is no longer larger than its size (i.e. the point at which it ceases to be a black hole)? Will the mass of the black hole 'snap' back into 'normal' space (from 'quantum space'), for lack of better words.
     
  2. jcsd
  3. Sep 21, 2007 #2
    Just to be perfectly clear, how about you explain what you mean by "its size"?
     
  4. Sep 21, 2007 #3
    I think what I mean is its volume, or the radius of its volume. I'm not really sure actually.
     
  5. Sep 21, 2007 #4

    mgb_phys

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    As a black hole shrinks it's temperature rises, so it's final mass will be emitted as gamma rays.
     
  6. Sep 21, 2007 #5
    So - are you implying that a black hole will remain a black hole until it evaporates its last bit of matter?

    That really doesn't seem to make sense... wouldn't it, at some point lose enough matter that it would stop being a black before it lost all its matter?
     
  7. Sep 21, 2007 #6
    No. Any amount of mass can be a black hole, as long as its confined to within its Schwarzchild radius.
     
  8. Sep 21, 2007 #7
    I think the original question was what would happen once it was no longer confined to within its Schwarzchild radius... no?
     
  9. Sep 21, 2007 #8

    mgb_phys

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    The Schwarzchild is proportional to mass, so as the mass decreases it's radius decreases until it 'classically' dissapears.
    As it gets very small quantum effects start to matter and at some point the final mass energy escapes as a couple of gamma photons.
     
  10. Sep 21, 2007 #9
    I've always wondered about the formation process more than the end. In particular, from the point of view of an asymptotic observer, in-falling matter will take forever before crossing the event-horizon. This includes the initial collapse. However, it will start to Hawking radiate all the time, as soon as there is curvature. In fact, it seems the black hole will evaporate before in-falling matter gets to the event horizon.
     
  11. Sep 21, 2007 #10

    mgb_phys

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    The point of view of the infalling matter is irrelavant - the universe doesn't care!
    Forming a black hole is easy - you just have to push matter together, closer than the Schwarzchild limit before the nuclear force can push it apart.
    You only have to worry about evaporation for very small holes - this is a good thing, it stops any small holes formed by cosmic rays in the atmosphere from growing!
     
  12. Sep 21, 2007 #11
    Yes - this was the original question.

    In response to this:

    Yes - I understand that the Schwarzchild radius is proportional to the mass. But I thought that the Schwarzchild radius was more of a theoretical concept - not a physical measure.

    EDIT: I guess I should clarify - I know that the Schwarzchild radius can be manifested as a physical measure - namely the event horizon. But I also thought that the schwarzchild radius could be independent of the radius of the volume of the mass contained in an object.
     
    Last edited: Sep 21, 2007
  13. Sep 21, 2007 #12

    mgb_phys

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    It's about the only physical measure of a blackhole. It's basically the point at which sensible classical physics stops - inside this radius everything gets a bit silly.
     
  14. Sep 21, 2007 #13
    But - anything has a schwarzchild radius, correct? The sun has a schwarzchild radius which is much smaller than the size of the sun. I'm saying 'size of the sun' because I'm not sure what measurement that actually is. I'm assuming that it is the 'radius of the volume of the sun.'

    With a black hole, it's just that the schwarzchild radius is larger than the 'size of the blackhole' before it actually turns into a black hole. At that point, what happens?
     
  15. Sep 21, 2007 #14
    With a black hole, the mass has zero volume, since no know physical process can stop the inwards collapse. So no matter how much mass you lose to evaporation, the matter inside is still smaller than the Schwarzchild radius.
     
  16. Sep 21, 2007 #15

    mgb_phys

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    Yes everything has a value for the schwarschild radius, ie the size it would have if it were to be squashed down to form a blackhole.
    The definition of a black hole is that it has mass 'm' inside it's schwarschild radius.
    For something where this has happened the schwarschild radius = the event horizon, has a definite physical meaning.

    The schwarschild radius is the boundary at which the escape volocity is greater than c, so inside this radius classical physics doesn't work, outside this radius you can still do the sums.
    In practical terms not a lot actually happens as a the size goes below the radius and it becomes a black hole, the gravitiational effects of a star squeezed into a size just slightly larger than it's black hole radius are still pretty extreme.
     
    Last edited: Sep 21, 2007
  17. Sep 25, 2007 #16
    I take this to mean then, that the radius of a star can be one foot (or one mile, doesn't matter) larger than the Schwarzschild radius. Does anyone theorize that it can be one foot less than the Schwarzschild radius, or do all theories assume zero volume of any mass that is within an event horizon? In other words, does current physics predict a sudden catastrophic collapse the moment mass is squeezed smaller than the BH radius, or is this a mathematical artifact of the "singularity" (infinity) problem of GR?
     
  18. Sep 25, 2007 #17
    All this stuff is in any textbook on the subject. You cannot expect PF members to recite what books take chapters to explain.

    You seem to still be in a state confusion over the different times experienced by different points of view. For someone standing on the surface of a collapsing star, nothing extraordinary (as far as gravity goes, there's all sorts of stellar stuff flying about) happens. They can't even tell when they've passed the event horizon. However, they will measure a finite amount of time (as they would by looking at their watch), before they reach the singularity. At which point, our current physics doesn't say what happens.

    From an observer far away, the surface of the star red-shifts out to black. As it happens, this is exponentially fast -- for a typical star, the time taken to go from 1.5x the event-horizon radius to the point where the last photon (taking into account the discreteness of energy) is likely to be emitted is about 10^-4 seconds. Furthermore, it becomes impossible to interact with the in-falling stellar surface. A photon launched at the stellar surface won't reach it before the stellar surface crosses the event-horizon.

    Now, it's certainly possible for a star to have a size just above its Schwarzchild radius. It is even possible for it to be below -- though only for a finite amount of time as seen by the star. For everyone else, the star collapses to the size of the Schwarzchild radius, and then cannot be interacted with any more, so we call it a black hole. For external observers, there is no point in talking about stars smaller than their Schwarzchild radius, because there's no observational way to distinguish them -- they're all the same hairless hole.
     
  19. Sep 25, 2007 #18
    Sorry for the inconvenience, I seem to have misplaced my textbooks 40 years ago.
     
  20. Sep 26, 2007 #19
    I tend to get mine out from a library when I need them...
     
  21. Sep 26, 2007 #20
    First, I wish to say that I appreciate your taking the time to answer my question. Neither you nor anyone else on the forum is obligated to answer anything, if you feel a question is stupid, or obvious, or too much trouble. So my appreciation for the time you took is genuine.

    I find great value in being able to ask questions and have experts such as you and others share their knowledge. In this particular instance however, I felt berated for having asked a question, and am less likely to ask one in the future as a result, which saddens me.

    If, as you put it, no one on this forum is going to take the time to answer questions that physics books devote chapters to, or that can be answered by researching textbooks in the library, then I suppose I have misunderstood the purpose of these forums. It was my understanding that discussions should be precisely about those things, and not about theories not found in textbooks.

    You certainly have the option of ignoring a question if you find it offensive or beneath discussion, and I believe most laymen asking questions here would prefer that to condescension.
     
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