On the nature of the "infinite" fall toward the EH


by rjbeery
Tags: fall, infinite, nature
stevendaryl
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#415
Dec23-12, 09:24 AM
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Quote Quote by zonde View Post
"Degeneracy of matter" does not tell us why it happens. It just tells that it happens.

Look, Pauli exclusion principle says that no two identical fermions can occupy the same quantum state. It does not tell us what would happen if two identical fermions would try to occupy the same quantum state. Currently we have no idea why the nature behaves that way.
I don't understand why degeneracy would have any relevance to black hole event horizons. Are you thinking that matter falling toward the event horizon would run out of states, and so the Pauli exclusion principle would prevent a collection of Fermions from falling further? If that's what you're thinking, then that's not correct. Nothing special happens at the event horizon that would force matter to become degenerate.
PAllen
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#416
Dec23-12, 09:53 AM
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Quote Quote by zonde View Post
"Degeneracy of matter" does not tell us why it happens. It just tells that it happens.

Look, Pauli exclusion principle says that no two identical fermions can occupy the same quantum state. It does not tell us what would happen if two identical fermions would try to occupy the same quantum state. Currently we have no idea why the nature behaves that way.

And there is still some room for interpretation. QM gives quite abstract definition for "quantum state". From wikipedia article about quantum state:
"In quantum physics, quantum state refers to the state of a quantum system. A quantum state is given as a vector in a vector space, called the state vector."

Well, we consider particles to be physical entities but quantum state is defined as mathematical entity. So it seems that Pauli exclusion principle is not very rigorous. This leaves (at least for me) the question open how we should model quantum state in real space (space-time).
What does any of this have to do with horizon formation for millions of galactic center BH, each with mass of millions to billions of suns. The issue here is that matter density for the aggregate at SC radius is much less than stellar atmosphere density, let alone stellar centers or neutron stars. How does degeneracy even become relevant?
PeterDonis
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Dec23-12, 12:28 PM
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Quote Quote by zonde View Post
Well, we consider particles to be physical entities but quantum state is defined as mathematical entity. So it seems that Pauli exclusion principle is not very rigorous. This leaves (at least for me) the question open how we should model quantum state in real space (space-time).
Quantum states *are* modeled using real spacetime; spacetime position is part of the description of a quantum state. The Pauli exclusion principle does not prevent two fermions of the same particle type from being in the same spin state at two different spacetime positions; it only prevents two fermions of the same particle type from being in the same spin state at the *same* spacetime position.

Actually, even that is not really the right way to say it. The Pauli exclusion principle as we have stated it is not a fundamental law; the fundamental law is that fermion wave functions are antisymmetric under particle exchange, whereas boson wave functions are symmetric. If I have a boson, say a spin-0 particle, at spacetime position x, and another spin-0 particle of the same particle type at spacetime position y, the wave function is symmetric under exchange of those two particles. But if I have a fermion in a definite spin state, say a spin-up electron, at spacetime position x, and another spin-up electron at spacetime position y, the wave function is antisymmetric (i.e., it changes sign) under exchange of those two particles.

The Pauli exclusion principle, which says that the wave function is identically zero if x = y, is an obvious consequence of the antisymmetry. However, it's not the only consequence; another consequence is that as x and y get closer together, the amplitude of the wave function decreases. That's what causes degeneracy pressure.

But all of that is below the level that GR models anyway. GR doesn't care about the microscopic details of matter; all it cares about is the stress-energy tensor. Degeneracy pressure, from the standpoint of the stress-energy tensor, works just like any other kind of pressure. The only real difference is the equation of state, i.e., the relationship between pressure and energy density.
zonde
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Dec24-12, 01:55 AM
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Quote Quote by DaleSpam View Post
OK. I am fine with all of this, but I am still missing the connection with how any of this prevents the formation of the EH. I could see it preventing the formation of the singularity, but not the horizon.
Formation of EH relies on idea that gravitating object can get more compact without any change to physical laws. But degeneracy of matter becomes more important at more compact configurations of matter.

Quote Quote by PAllen View Post
What does any of this have to do with horizon formation for millions of galactic center BH, each with mass of millions to billions of suns. The issue here is that matter density for the aggregate at SC radius is much less than stellar atmosphere density, let alone stellar centers or neutron stars. How does degeneracy even become relevant?
To discuss scenario like this we would have to have some idea how we would model occupied and available quantum states as we add more particles to given ensemble of particles. Or what happens with occupied and available quantum states as two ensembles of degenerate matter approach each other.

Your assumptions seems to be that particles affect occupancy of quantum levels only over short distance.
I assume that occupancy of quantum level drops as inverse square law as we go further from the particle.
zonde
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Dec24-12, 05:14 AM
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Quote Quote by stevendaryl View Post
I don't understand why degeneracy would have any relevance to black hole event horizons. Are you thinking that matter falling toward the event horizon would run out of states, and so the Pauli exclusion principle would prevent a collection of Fermions from falling further? If that's what you're thinking, then that's not correct. Nothing special happens at the event horizon that would force matter to become degenerate.
I suggest you to reformulate your question. Because there is a problem with it as it is stated. As you refer to pre-existing event horizon you imply that it is formed as a result of runaway gravitational collapse i.e. you are begging the question. I already raised the issue in post #402. So DaleSpam agreed that we should talk about hypothetical formation of event horizon instead.
DaleSpam
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Dec24-12, 07:33 AM
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Quote Quote by zonde View Post
Formation of EH relies on idea that gravitating object can get more compact without any change to physical laws. But degeneracy of matter becomes more important at more compact configurations of matter.
This is relevant for the formation of the singularity, not for the formation of the EH. The singularity is an infinitely dense object, but an EH can form at arbitrarily low densities. For example, see Susskind's 12th lecture on GR (http://www.youtube.com/watch?v=fVqYlSNqSQk) from about 2:00 to about 2:03 (of course the whole series is good).

I.e. your assumption "Formation of EH relies on idea that gravitating object can get more compact" is not correct. The formation of the singularity relies on that, but not the EH. The EH can form with simply a very large amount of non-compact material and you do not need a singularity in order to obtain an EH.

So again, what would prevent the formation of the EH? Degeneracy won't do it, that would only prevent the formation of the singularity.
PAllen
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#421
Dec24-12, 10:51 AM
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Quote Quote by zonde View Post

To discuss scenario like this we would have to have some idea how we would model occupied and available quantum states as we add more particles to given ensemble of particles. Or what happens with occupied and available quantum states as two ensembles of degenerate matter approach each other.

Your assumptions seems to be that particles affect occupancy of quantum levels only over short distance.
I assume that occupancy of quantum level drops as inverse square law as we go further from the particle.
So we have new fundamental law of physics: the "stellar exclusion principle" that prevents gathering too many stars in the same large region??!! Remember, the EH forms before there is any singularity or even any high density anywhere in the formative collapsing mass.
PeterDonis
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#422
Dec24-12, 11:27 AM
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Quote Quote by zonde View Post
Your assumptions seems to be that particles affect occupancy of quantum levels only over short distance.
I assume that occupancy of quantum level drops as inverse square law as we go further from the particle.
So you're saying that quantum effects play a non-negligible part in the dynamics of stars that are separated by light-years? That, for example, quantum interactions between the Sun and Alpha Centauri affect the relative motion of those two stars?
zonde
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Dec25-12, 01:42 AM
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Quote Quote by DaleSpam View Post
This is relevant for the formation of the singularity, not for the formation of the EH. The singularity is an infinitely dense object, but an EH can form at arbitrarily low densities. For example, see Susskind's 12th lecture on GR (http://www.youtube.com/watch?v=fVqYlSNqSQk) from about 2:00 to about 2:03 (of course the whole series is good).

I.e. your assumption "Formation of EH relies on idea that gravitating object can get more compact" is not correct. The formation of the singularity relies on that, but not the EH. The EH can form with simply a very large amount of non-compact material and you do not need a singularity in order to obtain an EH.

So again, what would prevent the formation of the EH? Degeneracy won't do it, that would only prevent the formation of the singularity.
There are two ways how to arrive at situation where EH is supposed to form.
First, we can add more matter to given gravitating object while it's radius is not increased too much by this addition.
Second, we can make given gravitating object more compact while it's mass is not reduced too much by this compactification.

I guessed that you was talking about the second scenario. If you are considering first scenario and want arguments concerning this scenario in particular please say it so that I don't have to guess.
zonde
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Dec25-12, 01:44 AM
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Quote Quote by PAllen View Post
So we have new fundamental law of physics: the "stellar exclusion principle" that prevents gathering too many stars in the same large region??!! Remember, the EH forms before there is any singularity or even any high density anywhere in the formative collapsing mass.
New? Why new? I am just extrapolating existing law.
zonde
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#425
Dec25-12, 02:02 AM
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Quote Quote by PeterDonis View Post
So you're saying that quantum effects play a non-negligible part in the dynamics of stars that are separated by light-years? That, for example, quantum interactions between the Sun and Alpha Centauri affect the relative motion of those two stars?
No, I am not talking about dynamics of stars but about dynamics of particles.
So what I say is that if we have two fairly degenerate stars approaching each other then whey would melt first and after that will start to evaporate. Or alternatively will fall into pieces depending on homogeneity of star.

If particles can't remain in their quantum states they can't maintain their collective structure. Kind of obvious IMO.
DaleSpam
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#426
Dec25-12, 06:42 AM
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Quote Quote by zonde View Post
I guessed that you was talking about the second scenario. If you are considering first scenario and want arguments concerning this scenario in particular please say it so that I don't have to guess.
I am considering any scenario where an EH forms. If there are multiple ways for an EH to form then a mechanism for preventing EH formation has to prevent all of them.

In general an EH forms whenever there is enough mass inside the Schwarzschild radius. That can happen at any density, so a mechanism which prevents high densities, like degeneracy, simply cannot prevent EH formation in general.
stevendaryl
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#427
Dec25-12, 11:00 AM
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Quote Quote by zonde View Post
I suggest you to reformulate your question. Because there is a problem with it as it is stated. As you refer to pre-existing event horizon you imply that it is formed as a result of runaway gravitational collapse i.e. you are begging the question. I already raised the issue in post #402. So DaleSpam agreed that we should talk about hypothetical formation of event horizon instead.
I'm not begging the question. I'm asking you a question. Why do you believe that degeneracy has anything to do with the formation of an event horizon? You can certainly make up your own theory, but there is nothing in General Relativity that would suggest that. If you're not talking about General Relativity, then what are you talking about?
stevendaryl
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#428
Dec25-12, 11:07 AM
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Quote Quote by zonde View Post
No, I am not talking about dynamics of stars but about dynamics of particles.
So what I say is that if we have two fairly degenerate stars approaching each other then whey would melt first and after that will start to evaporate. Or alternatively will fall into pieces depending on homogeneity of star.

If particles can't remain in their quantum states they can't maintain their collective structure. Kind of obvious IMO.
If you are making up your own theory of gravity, then I think this is not the appropriate place to talk about it. If you are talking about mainstream physics, then it is well understood that degeneracy prevents further collapse for any star less massive than the Chandrasekhar limit (described here: http://en.wikipedia.org/wiki/Chandrasekhar_Limit).
PeterDonis
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Dec25-12, 12:21 PM
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Quote Quote by stevendaryl View Post
it is well understood that degeneracy prevents further collapse for any star less massive than the Chandrasekhar limit (described here: http://en.wikipedia.org/wiki/Chandrasekhar_Limit).
Small technical point: the Chandrasekhar limit applies to white dwarfs, i.e., to objects in which electron degeneracy is the primary mechanism resisting compression. The analogous limit for neutron stars, where neutron degeneracy is the primary mechanism, is the Tolman-Oppenheimer-Volkoff limit:

http://en.wikipedia.org/wiki/Tolman%...3Volkoff_limit

Conceptually, both limits work the same, but the details are different because of the different types of fermions involved (neutrons vs. electrons).
PeterDonis
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#430
Dec25-12, 12:24 PM
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Quote Quote by zonde View Post
So what I say is that if we have two fairly degenerate stars approaching each other then whey would melt first and after that will start to evaporate. Or alternatively will fall into pieces depending on homogeneity of star.
Do you have any actual argument for why this would happen? Why would a degenerate star suddenly start melting? If the two degenerate stars collide with each other, then I could see matter being ejected from the collision; but if the stars are just free-falling towards each other, what difference would that make to their internal structure? The quantum states inside the star don't "know" that the two stars are approaching each other, unless they actually collide.
PeterDonis
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#431
Dec25-12, 12:26 PM
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Quote Quote by zonde View Post
Formation of EH relies on idea that gravitating object can get more compact without any change to physical laws.
Huh? This makes no sense. The physical laws involved are the Einstein Field Equation and the equation of state for the matter. It is well known that there are a range of reasonable equations of state that allow a gravitating object to get compact enough to form an EH; there are both analytical solutions and numerical simulations that show this. The laws certainly don't need to "change" at any point during the process.
PeterDonis
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#432
Dec25-12, 12:28 PM
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Quote Quote by zonde View Post
As you refer to pre-existing event horizon you imply that it is formed as a result of runaway gravitational collapse i.e. you are begging the question
Since there are already known solutions of the EFE with various equations of state that show runaway gravitational collapse, assuming it is possible is not begging the question.


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