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Pauli Exclusion Principle and Black Holes

  1. Feb 3, 2012 #1
    I understand that there may be no answer to the question "Why is Pauli Exclusion Principle not applied beyond a Neutron Star's mass?" since there may not be a full quantum gravity theory yet, however, I'm thinking, what if Pauli Exclusion Principle is not really a principle, but an indication that there is a force, a strong reactive force to the formation of Black Holes that can be overcome only under extreme masses?
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  3. Feb 3, 2012 #2
    Because after the degeneracy of a neutron star, the gravity is strong enough to overcome whatever force is holding the matter up, the Pauli-exclusion principal or the electro-magnetic repulsion of particles just isn't enough, gravity is too strong, and what actually happens after the degeneracy of a neutron star is unknown.
  4. Feb 4, 2012 #3


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    The fact is that we simply don't know what happens beyond the event horizon of a black hole. Is there a singularity? Is there some sort of exotic super unstable matter made out of quarks and leptons that is only made stable via the immense force of gravity? Perhaps constant creation-annihilation events? No one knows.

    Anyways, saying that the pauli exclusion principle doesn't hold up beyond a neutron stars mass may or may not be true. I know I've read about theorized stars composed of quark matter which is even denser than neutrons. Since these have yet to be observed we just can't say either way yet.

    Unlikely. To my knowledge the principle only describes the fact that the wavefunction of two identical spin 1/2 particles cannot overlap exactly. Something to do with one of them having to be anti-symmetric to the other. I'm not real sure on the details. See here for more: http://en.wikipedia.org/wiki/Exchange_interaction
    Last edited: Feb 4, 2012
  5. Feb 4, 2012 #4
    I'm not an expert in this. But I've also heard something about "degeneracy pressure" which is also mentioned by those posted.

    In a white dwarf, the factor that resists collapse is the electron degeneracy pressure. But when the mass has reached certain level electron degeneracy pressure is not enough, leading to further collapse into a neutron star. Whereby, electrons are caught by protons and become neutrons via process similar to Beta reaction. And on that occasion neutrons would provide degeneracy pressure which is stronger.

    And theoretically, there are quark stars, but they are not discovered by any means.

    Well, in my perspective, Pauli exclusion just says that free fermions are not likely to be in the same state, but under immense potential they can be forced to collapse.

    But in the sense of black holes, we have no means to determine whether matter in black holes are still in the form of fundamental particles.
  6. Feb 4, 2012 #5
    Hmm, that's what I use to think that too, but electrons can actually exist inside the nuclei of atoms without fusing with them due to their wave mechanics, and they are in a higher energy state if they are forced below their ground state.
  7. Feb 4, 2012 #6
    If you can believe it, I've had this thought too. Specifically, that perhaps another avenue and approach to quantum gravity is by considering the relationship between the Exclusion principle and the shape of space time. We know these two things are related even without considering black holes; they are in a balance during normal star operations in the form of "degeneracy pressure."

    Perhaps it isn't that deep, but I think some thought should go in this direction.
  8. Feb 4, 2012 #7
    But I don't think that it is so in this case. Under immense gravity, this type of beta decay is very possible. And I think that this reaction is energy releasing (well, not quite sure); therefore, it more likely to happen.

    I haven't learnt about anything about that "below state". I think that the orbital angular momentum number was said to be 1 less than the principle quantum number (which is the total angular momentum, characterized by OAM operator L2). With smaller principle quantum number, how is the system possible (because L2 is always positive)?

    I am just being a little skeptical here. I am most likely to be incorrect.
  9. Feb 4, 2012 #8
    What if Quark Stars are Black Holes and the Event Horizon coincides with the demolition of the Pauli Principle?
  10. Feb 5, 2012 #9


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    Inverse beta decay does not release energy. It takes an electron, combines it with a proton and forms a neutron, which is more massive than the proton and the electron, so it requires energy to create. My understanding is that under the pressures at neutron star density, it is simply more favorable to occur because it would require MORE energy for the electron to remain outside the nucleus in those conditions. In degenerate material, as the pressure increases the electrons are pushed closer together, but also acquire more energy, as the HUP says that since their position is constrained more and more then their momentum must become more uncertain. At a certain point the energy of the electrons become so great that inverse beta decay starts.


    As far as I know, a quark star would be more dense than a neutron star, but not have an event horizon yet. If it did, then it would be a Black Hole and not what we call a Quark Star.
  11. Feb 5, 2012 #10
    Oh, sorry, I didn't look upon those. But if electrons have higher energy out side the nucleus, does it mean that, in the situation, electrons' relativistic mass is greater than those in normal atoms?

    And I don't think that quark stars have already become black holes, since inside the event horizon, particles cannot communicate; therefore, in my perspective, no repulsion is likely to build up between quarks.
  12. Feb 5, 2012 #11


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    I don't think there's any reason to talk about relativistic mass, as that is an outdated concept as far as I know. (Or at minimum it is just confusing) I'd just stick to energy to keep everyone on the same page. Anyways, the electrons in degenerate matter are all jam packed into lots of energy levels in a way that is different from normal matter. In these higher energy levels the electrons have much more energy than they could in normal matter I believe.

    What do you mean? Particles inside the event horizon can and do communicate with each other. It is quite possible for you to fall inside the event horizon of a supermassive black hole and still be alive, as the gravitational gradient is very small.

    But more to the point, even if the matter inside a black hole was in a quark degeneracy state, it would still be called a black hole, as it has an event horizon for light. If it did not have an event horizon then it would not be a black hole.
  13. Feb 5, 2012 #12
    Sorry, I mean near the singularity. In models schwarzschild black hole, the light cones end at the singularity point and therefore the particles near the singularity would collapse.
  14. Feb 5, 2012 #13


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    At that point current accepted models simply break down. There isn't any way to know at this point in time.
  15. Feb 6, 2012 #14


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    The standard theory of black holes emerging from stars assumes that the Pauli principle IS valid in black holes.
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