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Black hole creation process

  1. Dec 11, 2014 #1
    We have a large mass, and we increase it slowly- dropping in one atom at a time. Will a black hole form suddenly, or will it gradually become blacker with the addition if each atom?

    I assume that a mass marginally below the threshold must at least partially have the properties of a black hole?

    Thanks
     
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  3. Dec 11, 2014 #2

    Matterwave

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    Creation of a black hole is quite catastrophic. It is not a gradual process. Degeneracy pressure can hold up the mass until it can't, at which point the mass basically crumples and catastrophically collapses into a black hole. Before the mass collapses, it can be quite dense, like a neutron star, but it is not dense enough to capture light and so is not "black", but it will become dense enough to redshift light emerging from the surface, so it does get redder.
     
  4. Dec 11, 2014 #3

    Doug Huffman

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    Your 'marginally' embraces the Sorites paradox, less one is it still marginally, less two, et cetera. I believe that your hypothetical would cause a catastrophe.

    LOL quite a coincidence of both using catastrophe.
     
  5. Dec 11, 2014 #4

    PeterDonis

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    As Matterwave said, the process of forming a black hole is not gradual; there are abrupt transitions in the state of the matter. If we assume that no nuclear, chemical, or other reactions occur, and there are no thermal fluctuations (for example, we drop iron atoms at absolute zero onto a mass composed, at least at low masses, of other iron atoms at absolute zero), there are still at least three abrupt transitions we will observe, and a fourth that also qualifies as a transition even if it isn't necessarily abrupt:

    (0) The transition from an object whose mass is too low for its own self-gravity to be significant, like a rock, to an object whose mass is large enough for self-gravity to be a significant factor in its structure, like a planet. This transition may not be abrupt; there are examples in nature of objects at various points along this spectrum (from rocks to asteroids to "dwarf planets" to planets).

    (1) The transition from normal matter, made of atoms and held up against gravity by ordinary inter-atomic forces, to white dwarf matter, made up of electrons and nuclei not organized into atoms and held up against gravity by electron degeneracy pressure. This is an abrupt transition; there is no stable sequence of intermediate states in between ordinary matter and white dwarfs.

    (2) The transition from white dwarf matter to neutron star matter, which is made of neutrons (electrons and protons are collapsed into neutrons during the process of neutron star formation) and held up against gravity by neutron degeneracy pressure. This is also an abrupt transition.

    (3) The transition from neutron star matter to a black hole, when the mass of a neutron star exceeds the maximum possible mass at which the star can hold itself up against gravity. The basic reason there is such a maximum mass is that, as the mass increases, the neutrons get squeezed closer together and become relativistic, and relativistically degenerate matter has a lower adiabatic index (the exponent in the equation of state relating pressure and density) than non-relativistically degenerate matter. So as the density continues to go up as the mass increases, the pressure can no longer increase fast enough to keep up, and a point is reached where the star is no longer stable and collapses. This is an abrupt transition.

    A neutron star near the maximum possible mass (and therefore the minimum possible size) will have some gravitational redshift, but it will be fairly small by black hole standards; there is a large gap between the properties of such an object and the properties of a black hole with a mass just above the maximum possible neutron star mass.
     
  6. Dec 11, 2014 #5
    One thing I don't understand is: Is it the imploding mass that causes a black hole to form, or is it the huge spacetime curvature formed around the imploding mass that causes the BH to form? In other words, if there were no spacetime for the mass to curve, would a BH actually ever form?
     
  7. Dec 11, 2014 #6

    PeterDonis

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    Then we wouldn't be discussing General Relativity, we'd be discussing some other theory. Do you have one? If not, your question doesn't really have any point, because if we don't have a theory to constrain our speculations, we can say anything we want.
     
  8. Dec 11, 2014 #7

    bcrowell

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    The OP asked about a hypothetical process, but the replies talk about gravitational collapse of a star. Gravitational collapse of a star doesn't have to be the way a black hole forms. For example, there could be primordial black holes that were formed shortly after the big bang, long before stars formed.

    There is no threshold, no minimum mass for a black hole. General relativity allows black holes to exist with any mass whatsoever. However, the known pathways to formation of a black hole from a dying star are pathways that only work if the star is fairly massive.

    Hypothetically, one could have a black hole of any tiny size, and then any matter that you trickled into it would simply increase its mass from there.
     
  9. Dec 11, 2014 #8
    The first part of my question is within the context of GR:

    The second part:


    .. is speculation on my part based on incomplete or misunderstood knowledge of the first part of the question, which is why I asked in the first place. Do you have an answer for the first part of my question?
     
  10. Dec 11, 2014 #9

    PeterDonis

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    The black hole is the spacetime curvature that is formed by the imploding mass.
     
  11. Dec 12, 2014 #10

    PAllen

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    To add to bcrowell's point, there is no minimum size to the Oppenheimer-Snyder collapse. In lay terms, that means if you posit matter that is incapable of pressure, then any amount of it will eventually (smoothly) collapse to a BH. General relativity does not include any theory of matter. Classical use of GR typically assumes that matter must locally behave as expected by SR (e.g. the dominant energy condition). However, this places no requirement on pressure, so the perfectly smooth (non-catastrophic) collapse of 1 gram of pressure-less mathematical dust to a BH is allowed in classical GR.

    Peter's comments apply to matter as we know it, governed by equations of state based on the standard model of particle physics.

    [edit: The closest real world analog I can think of the pressure-less dust is iron filings. Iron is incapable of either fission or fusion. If you add iron to an iron ball slowly enough to dissipate heat (which toward the end will be enormous ), the first catastrophe will be collapse from ordinary matter to neutron star with release of a flood of neutrinos. This would constitute some weak form of supernova (which obviously has never been observed). Then, as you kept adding iron, at somewhere above 3 solar masses, you would get catastrophic collapse to a BH. These are best guesses, as there is no process in the universe that slowly accumulates iron.]
     
    Last edited: Dec 12, 2014
  12. Dec 12, 2014 #11
    The question was about dropping in one atom at a time... and the nature of the beginning of the thing becoming a BH.

    It seems to me that the OP might be wondering:

    Will the transition to BH happen after the addition of one particular atom in the series of atoms added?
    (assuming that each dropping of an atom is spaced apart in time sufficient for its effect to be fully made manifest.)

    Or better yet, let the things being dropped in be protons or hydrogen atoms... so the increment is small.

    I think the OP is wondering if the pre-BH object is subject to HUP fluctuations and wondering how the addition of a single increment compares to the magnitude of these fluctuations... whether a fluctuation might be sufficient to put the object over the critical mass to become a BH when the BH is in the state where the addition of one more increment of dropped matter would otherwise do so...

    Since the size at which an incrementally built BH is known, what orders of incremental mass compare to the fluctuation magnitude?

    Could an object that is just short of becoming a BH make the transition through a HUP fluctuation?

    Also, as to micro BHs, I don't know if it is thought that there are micro-versions of the above - micro objects just short of the density to become a BH. If so, would their HUP fluctuations with respect to their size be bigger than the large BHs? If so, it seems they would very subject to making the transition, and so quite rare in their pre-BH state.
     
  13. Dec 12, 2014 #12

    PAllen

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    I would say much of this is unknown. Even the minimum mass of BH you would get by incrementally growing a neutron star is unknown (3 to 5 solar masses is an estimate, but that is an error bar of a whole sun). Qualititatively, all agree (including my hypothetical adding iron to a neutron star), that the final collapse to a BH would be sudden.
     
  14. Dec 12, 2014 #13
    By "sudden", does that mean at the speed of sound through the material of the object, or more like the speed of light around the surface... or does the geometry of the BH make the usual space and time measures confounded by the variations of an observer's position and motion? Maybe the transition must always appear "instantaneous"?
     
  15. Dec 12, 2014 #14

    PAllen

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    I don't know of any real analysis of a model of incremental BH formation from a neutron star (it would be a lot of work, and since it isn't known to occur, maybe no one has been motivated). Or maybe I've missed it in the literature. So I really can't answer the 'how fast' question with any confidence. It may not make much difference because the speed of sound would be a significant fraction of the speed of light for a neutron star (e.g. > .3 c).

    On the other hand, viewed from afar, the process would be slower, but not really that slow - the object would become blacker than CMB filled empty space relatively fast, but much slower than as experienced by an particle of the neutron star.
     
  16. Dec 12, 2014 #15
    so, are there any spacetime-free solutions for mass/energy?
    And if there are, what woud it say about an imploding mass?
    Would we get to observe a mass collapse without becoming a black hole?
     
  17. Dec 12, 2014 #16

    martinbn

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    Just one more comment. If the characteristic feature of a black hole is the event horizon, then you can get a black hole without anything unusual happening, at least for some time. Take a spherical configuration of stars that fall towards the centre. If you choose the masses well, an event horizon will form at the centre and grow outward i.e. you have a black hole. If you are somewhere there you will not see anything unusual. In fact a horizon may be growing and passing through you room right now.
     
  18. Dec 12, 2014 #17

    PAllen

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    What do you mean by spacetime free solutions? Since SR and GR are built on spacetime, that seems to be asking what theory would be true if the currently best verified theories were wrong? There is no meaningful way to answer that. It is not like picking matter without electric charge, which is possible. There is just no theory left if you remove spacetime.
     
  19. Dec 12, 2014 #18

    PAllen

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    Yes, I've used this example many times (stars as dust; implements hypothetical smooth Oppenheimer-Snyder type collapse), as a way of talking about what you would see throughout a collapsing volume, and also to discuss how radical a change to classical GR is implied by 'active horizon' hypotheses (e.g. firewalls).

    [edit: similarly, if allowed to pose implausible initial conditions, if you had a sufficiently large sparse dust cloud, with a uniform density of e.g. air, but of a size just short its being in its own SC radius, then it would smoothly collapse further, with growth of event horizon from center, without any happening to the dust until well after it was already inside its event horizon.]
     
    Last edited: Dec 12, 2014
  20. Dec 12, 2014 #19

    PeterDonis

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    Wouldn't you pass through a white dwarf stage first? At that stage, the iron nuclei would still be separate entities, but the electrons would be degenerate. At the neutron star stage (the next stage), there would no longer be iron nuclei or electrons, just a big blob of neutrons. Ordinary iron ball -> white dwarf -> neutron star is the sequence according to the Harrison-Wakano-Wheeler equation of state (which is basically what we're talking about here--the discussion in Thorne's Black Holes and Time Warps is what I've been basing my comments on).
     
  21. Dec 12, 2014 #20

    PAllen

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    More like a black dwarf, with different composition than any that form naturally (none are iron). But, yes, I forgot the stage of electron degeneracy. The only stage that would release much energy is the neutron star formation, when an enormous surge of neutrinos are released.
     
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