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Must a black hole be a point singularity?

  1. Sep 28, 2010 #1
    If during star collapse the mass not blown away is large enough to form a black hole, shouldn’t the resulting extraordinary high temperature essentially convert all the mass into contained radiation? The basic pressure formula for this intense radiation would likely be P = pc*2 (where p is the equivalent mass density of the radiation). This should prevent collapse to a singularity since this radiation pressure has no limit and increases as density or 1/R*3, faster than the increase of gravitational force.

    (format test only: c squared = c*2 = c<sup>2</sup> )
  2. jcsd
  3. Sep 28, 2010 #2
    GR equations say, "yes" it must be a singularity, but there are certainly doubts. I think many believe that a workable framework of quantum gravity will eliminate the singularity from the equations, and our understanding of nature.
  4. Sep 28, 2010 #3


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    The singularity is "off the map", so to speak -- it doesn't have any shape itself, but we can talk about how the space around where it would be is defective.

    The space around a point-like hole has the same shape as the space around a ball-like hole -- there isn't really any difference between the two.

    (I think other shapes are possible -- e.g. a ring shape. The space around a ring-shaped hole really does look different than the space around a point-like hole)

    It's easy to see in two dimensions with polar coordinates. Normally, the set of all (r,theta) with r > 0 form a plane with a single point removed -- the origin.

    Now, do a change of coordinates, setting s = r + 1. Plotting the (s,theta) as polar coordinates now reveals an entire closed disk removed from the plane.

    Well, remember this is GR, not Newtonian gravitation. High pressure accelerates the collapse -- that is why a black hole can form in the first place! (at least, as I understand things)
  5. Sep 28, 2010 #4
    I think the question basically is: Can intense radiation pressure be the support mechanism inside a black hole? I think it is logical that when a star above several solar masses collapses, the neutrons in the core disintegrate into radiation and some quark matter. As the collapse continues and temperature rises still further virtually all matter converts to radiation. If the radiation is contained in the system, the pressure of the radiation should be P = pc*2 , where p is the equivalent mass density of the radiation. The contained radiation, which has mass, basically acts like a compressed gas that can generate pressures exceeding neutron collapse pressure.

    As I understand the TOV equation, dP/dr is proportional to p + P, which means if P is high enough there is runaway collapse. I don't think Einstein accepted this equation because he didn't believe in a point singularity.
  6. Sep 28, 2010 #5
    The only viable alternative to collapse into a singularity that exists in theory now, comes from String Theory... and that's not exactly coming with the developed pedigree of GR or QM. Given the "black" nature of the hole, it's probably best to concern ourselves with the event horizon on out.
  7. Sep 28, 2010 #6
    Oh no not the event horizon again. I'm still having nightmares about the last thread on this! :cry:
  8. Sep 28, 2010 #7


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    A singularity is a red flag in physics. It strongly suggest the mathematical model has 'broken' when singularities emerge in the solution. We know this for fact in GR, and suspect the same in QM. Reconciling GR and QM [quantum gravity] will give us a better idea how nature deals with her dirty laundry. I think we will ultimately arrive at a theory that transcends both GR and AM. Ptolemy's epicycles persisted for about 1500 years before we finally overturned that theoretical apple cart.
  9. Sep 28, 2010 #8
    Yup, present theories could push people over the edge. If a neutron star collapses to perhaps one tenth its volume, wouldn't we expect a dramatic increase in temperature? Wouldn't essentially all matter be converted to radiation? Matter changes dramatically above the temperature of quark production. Below this temperature we have matter with little energy; above this temperature we have radiation with little matter. Therefore above this temperature we should analyze the characteristics of radiation instead of matter.

    How would a huge distributed mass of radiation react to itself gravitationally? At the center of the distributed mass we would expect little gravitational force, only intense pressure. Gravitational forces would increase with radius, reaching a point where they would be strong enough to contain radiation, acting like the skin of a balloon. Schwarzchild radius.
  10. Sep 29, 2010 #9
    Doesn't help you. Remember that E=mc^2, so any radiation that you have also has mass, which means that it also has gravity.

    I'll leave it for you as an exercise, but you can show that if you have enough mass-energy in a small enough space, that the gravity created by that radiation is increase faster than any radiation pressure. The more radiation you have, the more gravitational force and once you hit some limits, then more radiation *increases* the collapse.
  11. Sep 29, 2010 #10

    Yes, and this is a bad thing if you are trying to halt a collapse. I give you a table made of wood. You jump on it, and the table stops you. If I give you a table made of laser light, and you jump on it, the laser light won't stop you.

    So the fact that the temperatures increase to the point where things start behaving like radiation is exactly why things collapse.

    Something that helps a lot is to just think of matter and radiation as the same thing. I have a pound of brick. Now suppose I turn it into energy by maybe combining it with a pound of anti-matter. The two pounds of photon gas *still* has the same gravitational pull.

    The way that people model this is to just model radiation as a photon gas, and just like any other gas, photon gas has weight and gravity. So what happens if I turn neutron star material into photon gas is that the gravity stays the same, but the pressure goes way down.

    Nope. E=mc^2. If you have a lot of E, you will still have a lot of m.
  12. Sep 29, 2010 #11


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    Well, if you turn the whole table into radiation, it will most certainly stop you. Actually, it will accelerate the particles that once were you away at a significant fraction of the speed of light. Kind of total protonic reversal.
    It's a good idea to get a much pressure as possible, if you don't mind the side effects. But it doesn't help.
    Actually, pressure gravitates, which means that radiation has the double gravitational pull.
    Radiation is unstable, it will either explode or contract to a "singularity". It can be proven that it will contract if it is enclosed in less that 9/8 of its Schwarzschild radius.
  13. Sep 29, 2010 #12
    "At the center of the distributed mass we would expect little gravitational force, only intense pressure."
    "Nope. E=mc^2. If you have a lot of E, you will still have a lot of m."

    At the center of the earth there is relatively trivial gravitational force, only intense pressure. Same with a neutron star.
  14. Sep 29, 2010 #13
    "I give you a table made of wood. You jump on it, and the table stops you. If I give you a table made of laser light, and you jump on it, the laser light won't stop you."

    If 1 gram of matter is contained in 1 cc, and then is totally converted into radiation, and this radiation is contained in the 1 cc, the expected pressure would be pcˆ2 = 10ˆ21 g/cmˆ3.
  15. Sep 30, 2010 #14


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    p= \rho c² = 10^14 J/cm³=10^20 Pa.
  16. Sep 30, 2010 #15
    Good, the kind of response I was looking for. I should have titled this thread instead "Can radiation pressure be the support mechanism inside a black hole?"

    Also I should have written 10^21 grams/cm^2 above, not 10^21 g/cm^3.

    Lets call pressure P, density = p = rho, volume V, mass m, light speed c.

    P would be the expected amount of radiation pressure in a closed system when mass is converted to radiation. Pressure, normally defined as F/A, also equals (available energy)/volume. If m is the amount of mass converted to radiation in a closed volume V, then P = mc^2/V. Since p =m/V, then P = pc^2. 1 gram of radiation contained in 1 cc would equal 9 X 10^20 gm/cm^2.
  17. Sep 30, 2010 #16
    Better phrased: 1 gram of radiation contained in 1 cc would create a pressure of 9 X 10^20 grams/cm^2.

    Its unconventional, but I think people should get used to saying grams or kilograms of radiation.
  18. Sep 30, 2010 #17


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    I can follow all your steps except this one:
    1 g * c² = 10^14 J (well, 9*10^13). So there's 10^14 J/cm³ = 10^20 Pa.

    What you seem to be doing is you take c in units of cm instead of m, and then claim that the so dereved unit of energy (actually 10-4 J) is grams. That doesn't work.

    EDIT: I just saw your second post and thus looked more closely. You're now talking about g/cm² as a unit of pressure. Don't do that. g/cm³ is non-SI, and it uses c=1, but at least it makes some sense.
    Last edited: Sep 30, 2010
  19. Sep 30, 2010 #18
    It's worth pointing out that geodesics become space-like within 2M (the Schwarzschild radius) so no matter how high the pressure is, unless geodesics are time-like within the collapsing matter (which I'm guessing when applying the Schwarzschild interior solution for masses that fall within 2M isn't the case) then a stable radius cannot be sustained within 2M regardless of the pressure, it would be like us hovering at 1.00 pm in time-like geodesics, it's just not going to happen. For the Schwarzschild solution, the only way the collapse can stop is if the energy that separates matter and space become indistinguishable and geodesics as we understand them become something different which is what is supposed to happen at Planck scale/density.
    Last edited: Oct 1, 2010
  20. Sep 30, 2010 #19
    I will probably restart this thread tomorrow with the title: "Can radiation pressure prevent collapse inside a black hole?"
  21. Sep 30, 2010 #20
    Ich, so we are on the same page, how would you prefer all of us to refer to pressure?:


    or kg/square meter

    or ?? ...... your suggestion

    Also, how would you prefer us to density? We can have a better discussion if we all use the same units and terminology.
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