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The paradox of Hawking radiation - is matter infinitely compressible?

  1. Sep 18, 2013 #1
    The hypothetical Hawking radiation means that a set of baryons can be finally transformed, "evaporate" into a massless radiation - that baryons can be destroyed. It requires that this matter was initially compressed into a black hole.
    If baryons can be destroyed in such extreme conditions, the natural question is: what is the minimal density/heat/pressure required for such baryon number violation? (or while hypothetical baryogensis - creating more baryons than anti-baryons).
    While collapsing into a black hole, below the growing event horizon, not only light but also matter has to travel toward the center: any finite limit for conditions is finally exceeded - so baryons should be destroyed there, releasing huge amount of energy (complete [itex]mc^2[/itex]) - pushing the core of collapsing star outward - preventing the collapse. And finally these enormous amounts of energy would leave the star, what could result in currently not understood gamma-ray bursts.

    So isn't it true that if Hawking radiation is possible, then baryons can be destroyed and so black holes shouldn't form?


    We usually consider black holes just through abstract stress-energy tensor, not asking what microscopically happens there - behind these enormous densities ... so in neutron star nuclei join into one huge, in hypothetical quark star nucleons join into one huge ... so what happens there when it collapses further? quarks join into one huge? and what then while going further toward infinite density in the central singularity of black hole, where light cones are directed toward the center?

    The mainly considered baryon number violation is the proton decay, which is required by many particle models.
    They cannot find it experimentally - in huge room temperature pools of water, but hypothetical baryogenesis and Hawking radiation suggest that maybe we should rather search for it in more extreme conditions?
    While charge/spin conservation can be seen that surrounding EM field (in any distance) guards these numbers through Stokes theorem, what mechanism guards baryon number conservation? If just a potential barrier, they should be destroyed in high enough temperature ...

    Is matter infinitely compressible? What happens with matter while compression into a black hole?
    Is baryon number ultimately conserved? If yes, why the Universe has more baryons than anti-baryons? If not, where to search for it, expect such violation?
    If proton decay is possible, maybe we could induce it e.g. by lighting the proper gammas into the proper nuclei? (getting ultimate energy source: complete mass->energy conversion)
    Is/should be proton decay considered in neutron star models? Would it allow them to collapse to a black hole? Could it explain the not understood gamma-ray bursts?
    Last edited: Sep 18, 2013
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  3. Sep 18, 2013 #2


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    No. There is no way for them to release the energy - apart from Hawking radiation, but that is completely negligible on the timescale of a core collapse.

    That is not true.

    There is no enormous density which would have anything "behind it". In addition, for events outside the event horizon it does not matter what happens inside.

    Huge what? What does that mean?

    It could be possible that baryon number violation can happen via virtual black holes. That is very speculative, however.

    The LHC looks for those processes, too, but the energy is probably not sufficient.

    That is unknown.
    Probably not.
    In particle physics experiments and proton decay searches.

    It is way too rare to be useful for that.

    Please do not randomly mix buzzwords to form questions.
  4. Sep 18, 2013 #3


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    You don't need anything nearly so exotic. You can just use a proton and an anti-proton, when they anhillate the two baryons are destroyed. This happens all the time.
  5. Sep 18, 2013 #4
    Even if that energy gets released, if it happens inside of the event horizon, it cannot push anything outwards because once you're inside all directions point to the center due to space-time curvature. That's how black holes work. There is no outwards direction. There is only inwards.
  6. Sep 18, 2013 #5
    This is standard argument - it is below the event horizon, so it doesn't matter what happens there - we shouldn't worry about it ...
    But shouldn't models be internally self-consistent? (another problem here is that in the central singularity, spacetime is no longer a manifold - GRT does not apply).
    The equations predict some density profile inside - of density of matter - there is some state of matter behind this density - what state is it?

    I have meant that in neutron star, the boundaries between nuclei vanish - the whole star is kind of a single huge nucleus. In hypothetical quark stars, boundaries between nucleons vanish - the whole star is kind of a single huge nucleon.
    What happens with matter when it collapses further?

    Indeed, I agree that there is a hope in colliers.
    Unfortunately observing proton decay there is extremely difficult - one way could be through energy balance, but the calorimetry is not precise enough. Another is through Monte Carlo simulations, but for that we would need to exactly know what are we looking for ...

    A different way is observing the neutron stars - if somewhere in the Universe there are extreme enough conditions, aren't the cores of the neutron stars the best candidates?
    So what should we expect?
    One scenario could be cyclic - first it compresses gravitationally, creating required conditions for baryon decay in the center and so a huge blast there - expanding the star and enclosing the cycle ...
    This energy is finally released as kind of gamma-ray bursts.

    If only a potential barrier holds baryons together, it could be a matter of finding the proper resonance to get out of the local energy minimum - of shining some very specific gamma rays at specific nuclei ...

    I don't know what "buzzwords" you are refereeing to, but I was just asking about taking violation of baryon number conservation, which I see you agree to, into neutron star models?
    What consequences should we expect?
  7. Sep 18, 2013 #6
    Proton - antiproton annihilation does not violate the baryon number conservation ... while the problem of hypothetical Hawking radiation is that you have a lot of baryons first, and zero after the "evaporation" - the baryon structure does not survive this compression.

    But if baryons can be destroyed, it would require crossing some finite energy barrier holding their structure together - it would not need formation of event horizon, could just happen in core of massive neutron stars.
    Just for stars massive enough, evolution would have one additional stage - of burning baryons - releasing huge amounts of high energy radiation: observed gamma-ray bursts.
  8. Sep 18, 2013 #7


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    Ah, yes, I see what you are saying. My understanding is that baryon number conservation may be only an approximate conservation law anyway in the standard model, i.e. at high enough temperatures I don't think that it violates the standard model.
  9. Sep 18, 2013 #8
    Indeed DaleSpam. While Gauss law says that electric field on any closed surface around defines electric charge inside - the whole EM field guards charge conservation and similarly for spin conservation ... is there a reason for ultimate conservation of baryon number?
    Baryons could be just some stable constructs - of quarks, some fields (gluons) - deep local minimums of some potential?

    It would mean that in some really extreme temperatures, like in the center of neutron star, they should thermodynamically "tunnel" to the global minimum of potential: vacuum, releasing the rest energy (mass).
    If so, maybe there could be a direct way to make this getting out of minimum more probable through finding some resonance ...
    Last edited: Sep 18, 2013
  10. Sep 18, 2013 #9
    The baryon gets destroyed under extreme conditions which requires a black hole in the first place.
    That is: Black hole exist => Baryons gets destroyed and not:
    baryons can be destroyed => black hole shouldn't exist. I believe it is a one way implication.
    And note that a pair of baryon (and antibaryon) is formed which mutually annihilate each other, but since the gravity →∞ and isn't actually ∞ some particules/energy can escape resulting the hawking radiation.
    But at a realistic scale of a black hole, the hawking radiation is negligible, unless your studying time interval →∞.
  11. Sep 18, 2013 #10


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    I did not say we should not worry about it. I just said it does not influence anything outside. And apart from the central point, the models are fine - general relativity can describe the whole spacetime inside apart from the singularity (or whatever might be there).
    During the collapse? Something complicated (check publications dealing with that). Afterwards? Vacuum.

    It collapses completely and becomes a black hole.
    By the way, neutron stars and even hypothetical quark stars still have outer regions with regular atoms.

    The observation of a proton decay at a particle accelerator is impossible. Way too much background. There is no point in it anyway - you do not need particle accelerators to get protons.

    Not hot enough I think.

    You are making up stuff here without any background. Please stop that, it violates the forum rules.

    If there is some energy scale where baryon number violation is frequent, it is probably the GUT scale at ~10^16 GeV, way beyond every reasonable we can do.
  12. Sep 18, 2013 #11
    So where exactly are baryons destroyed?
    Imagine baryon density profile - initially it should be close to energy density profile.
    Below the event horizon, even photons have to travel toward the center, so this profile should tend to Dirac distribution in the center.
    Also their total number should decrease due to Hawking radiation - so where is it happening?

    I think near the center - because of temperature/density/pressure?
    So what temperature/density/pressure are required to destroy baryons? Or create them while baryogenesis?
    If any finite, they can be obtained in the center of neutron star before collapsing into black hole - preventing this collapse ...

    Ok, thanks for nice finite number.
    So let us imagine collapse of neutron star into black hole.
    In some moment the surface gets below the horizon - where was the horizon before?
    Do neutron stars have event horizon in their center?
    The only reasonable explanation seems that the horizon in one moment quickly starts growing from the center?
    If so, in the central point there have to be exceeded any finite temperatures - including your "~10^16 GeV" ...
    Last edited: Sep 18, 2013
  13. Sep 18, 2013 #12


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    Baryon decays would not prevent a collapse. I think they would even reduce the pressure and make the collapse quicker.

    See my previous post.
  14. Sep 18, 2013 #13
    mfb, I have included reply in edit of the previous post: how do you think event horizon starts growing while collapse to the black hole?
    If from the center - any finite temperature would be exceeded there earlier - including your "~10^16 GeV" - it should start destroying baryons earlier.

    If so, large number of baryons would be destroyed there - locally increasing temperature/pressure - making that surrounding regions would also exceed this finite limit.
    Finally there would be large explosion in the center of neutron star - temporarily preventing the collapse and leading to cyclic bursts of high energy radiation ...

    Like here:http://mathpages.com/rr/s7-02/7-02.htm
    http://mathpages.com/rr/s7-02/7-02_files/image003.gif [Broken]
    Is there a finite temperature where and when this process starts?
    Last edited by a moderator: May 6, 2017
  15. Sep 18, 2013 #14


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    It does not start from the inside. This comes from the fact that the radius of a black hole is proportional to mass, while the mass inside a radius in a homogeneous volume grows with the radius cubed.
    Why should it exceed that temperature? Please provide a reference for claims like that.
  16. Sep 18, 2013 #15

    Baryons are destroyed (also can be said that energy is lost since we know that energy ⇔ to matter) beyond the event horizon AKA inside of the black hole; The baryons destroyed are the ones that are part of the black hole/singularity, and not the outer matter that resides on the limit of the EH.
    It is true that their total number is decreasing due to Hawking's radiation, i'd say it's near the center, because it's in the center where the majority of the mass and matter is located, specifically in the singularity where constant reaction of conversion of energies into 2 baryons and anti baryons and vice vera happens. I'm not sure about the numbers required to be able to cause this transformation which results in the destruction of bayrons, all I know is that it happens within the black hole specifically near the most dense areas (singularity).
    I do not think that baryogenesis takes place withing the black hole, because all bayrons inside of the event horizon are from an existing source; there's no creation of new bayrons only endless conversion energy⇔baryons+antibaryons.

    Usually the gravitational collapse can't be stopped; what do I mean? I mean when we say "Neutron star" usually it means that the star's core has reached a stable state of degeneracy pressure equilibrium in which it will not collapse into a black hole anyways.

    In case the core is from the start supermassive (>≈3xMs) it will collapse infinitely and nothing can stop it, and the baryons that you mean (if I understood correctly) can be destroyed to stop that collapse will not undergo the baryon destruction because this happens as stated before inside the event horizon which hasn't been formed yet; you can't destroy a baryon because the reason for it's destruction isn't created yet.

    The horizon did not exist before; you have the right to name an event horizon, only and only if, the black hole is formed.
    In the case of a neutron star the event horizon does not exist in any way. Think about it, you can see the neutron star, while by definition an event horizon is a barrier after which you can't see any event happening.

    Quite simply the event horizon isn't of a solid nature, or a barrier that is made of baryons that expands.
    The EH is a certain critical zone bent of the universe; in the photo you posted before (the one showing the Universe's distortion) the circle (base) of the cone is the event horizon and it differs from one black hole to another, based on its mass and thus its size.
  17. Sep 18, 2013 #16
    Ok, the deciding question is how the initial evolution of event horizon looks like.
    I have linked one webpage, here is another : http://astro.physics.sc.edu/selfpacedunits/Unit57.html
    and another: http://arxiv.org/pdf/1103.0835.pdf
    I couldn't find any serious sources yet. I thought that horizon should evolve in continuous way ... so maybe you could provide some sources or explain how event horizon could just emerge in one moment in nonzero radius?
    If so, I would agree with you that Hawking radiation does not contradict itself.

    But if event horizon has started in a point inside, as you have mentioned R=2GM/c^2, what means that density would have to be infinite there.
    Also the appearance of event horizon in this point would start Hawking radiation/baryon number violation - which has radiation temperature proportional to 1/M, meaning infinity while starting the event horizon ...

    update: A peer-reviewed paper also starting with R=0 horizon: http://download.springer.com/static/pdf/925/art%253A10.1134%252F1.558970.pdf?auth66=1379720523_1733b779877918e34b4c1ae8ee089eaf&ext=.pdf [Broken]
    Last edited by a moderator: May 6, 2017
  18. Oct 17, 2013 #17
    So as something is collapsing, whatever the state of matter, it gets to a point where the amount of it within a particular radius is now enough to curve space time to the extent where all light cones point inward. That's a certain amount of material within a certain radius of a certain volume. A critical density is required for an event horizon to exist. Infinite density is not required. The event horizon isn't something that pops into existence, violating this or that conservation law. It is just our description of the place where space time obtains a specific curvature. It isn't contained in a neutron star because it doesn't have the sufficient density.
  19. Oct 18, 2013 #18
    Holesarecool, what radius?

    Ok, imagine there is a drilled/transparent hole to the center of neutron star, so you can see photons from all its internal layers down to the center of the star.
    What would you see inside this hole while the collapse?
    Event horizon in some radius r means that light from deeper layers can no longer overcome the gravity - would r grow from the center of star or just appear in some nonzero radius?
  20. Oct 26, 2013 #19
    It grows starting from r=0 at the center of the star (as you can clearly see in those diagrams you posted).

    The only odd thing is that it appears and starts to grow before the star has collapsed into a black hole. But that's fine - event horizons are not defined by local quantities. They are defined by the fact that light cannot escape them.
  21. Oct 26, 2013 #20
    Indeed, it was the reason I have posted them.
    The problem this thread is about, is that while the radius of event horizon is proportional to the mass inside, this mass is proportional to density times r^3 ... what means that density of matter has to reach infinity to start forming the event horizon. (r=2Gm , m~rho*r^3 -> rho ~ 1/r^2).

    The question is if matter can sustain such infinite compression?
    If baryon number generally can be violated (e.g. while baryogenesis or through Hawking radiation), shouldn't these baryons be destroyed before reaching this infinite density?
    It would release lots of energy and generally prevent the collapse ...
  22. Oct 26, 2013 #21


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    A black hole forms whenever a mass is compressed to a volume less than its Scwharzschild radius. Obviously, the density of matter inside need not be infinite.
  23. Oct 27, 2013 #22
    The point of no return for a neutron star collapsing into a black hole is when the mass is within r=9M/4, according to the Schwarzschild interior metric, this is the point when the time dilation at the centre of the star reaches zero. As the star collapses further, the radius where [itex]\tau=0[/itex] begins to move outwards from the centre towards the surface of the star, as shown in the diagrams in post #13 and 16, the space within this radius will be space-like and anything within will be pulled towards the singularity. You don't need matter to achieve infinite density to start the process, you simply need matter to fall within 9M/4 (which is 2.25M).
  24. Nov 12, 2013 #23
    No, it is not. As I said above, the event horizon can form and grows before there is any matter inside it at all.

    Your calculation is wrong. First, it only applies in static cases, not when matter is collapsing. And second, all it shows is that if the interior of the black hole had constant density, that density would scale as 1/radius^2 of the hole.
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