# Asymptotic Freedom in QCD and...

Discussion in 'Physics & Math' started by RajeshTrivedi, Sep 14, 2017.

1. ### riverValued Senior Member

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I was thinking , perhaps guons behave much like a liquid ( water for example ) , we are discussing three dimesional form . Since gluons are a liquid , to my thinking , it makes sense , how would that complicate the mathematical model of gluons , presently ?

(Therefore like an elastic band , the further you stretch the band the stronger it resists the stretch.)

Last edited: Nov 12, 2017 at 12:44 AM

3. ### RajeshTrivediValued Senior Member

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Since you were objecting, I thought you understood.
I will state it again.
When the Neutrons are compressed due to gravitational compaction, the gap between the constituent quarks reduces, this reduction in gap weakens the bond strength and energy release takes place. This energy radiates away from the object as the innermost all Neutron core is superconducting type and thus mass of the object reduces. This reduction in mass causes, reduction in Schwarzschild radius and the core never falls beneath its schwarzschild radius, thus no BH can form via the route of accretion of mass by a Neutron Star.

5. ### RajeshTrivediValued Senior Member

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Gluons are considered to be mass-less particles, as the force carrier between quarks. More like photons being force carriers in EM interactions.
Instead what I have proposed is that there exist something called PSMR (Progenitor State of Matter & Radiation). Gravity is nothing but stretch in PSMR. PSMR stretched beyond certain critical point forms the materialistic particles, and relaxation in stretched PSMR produces photonic radiation. Higher the stretch, higher the gravity. Gravity is variable, highest between quarks and naturally falls to prevalent level even between hydrogen nucleus and its electron.

This simple hypothesis, PSMR based, explains almost all the observations from Strong Interaction between quarks to relativistic jet emission, supernova etc. I have applied this hypothesis to Strong Interaction, Instability of larger Nucleus, Muonic Hydrogen, MM experiment, Red Shift, CMBR, Unruh Effect, Super Nova explosion, Jets etc, all are plausibly explained without any inconsistency.

7. ### riverValued Senior Member

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I'll leave it to yeah .

Hope your thinking works out to a better understanding of our Universe !!

river

8. ### NotEinsteinRegistered Senior Member

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Right, so the core of the neutron star turns into a big ball of quarks, all squished together. That's a big change from neutrons; is it still superconducting? Can it still be modeled as a perfect fluid?

Edit: And is the resulting object not just quark star?

Last edited: Nov 12, 2017 at 8:39 AM
9. ### RajeshTrivediValued Senior Member

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No.
First I would suggest, have a look at the easy to find wiki link on Neutron Star, straight away jump to 'structure" part. This will clarify that even as per present understanding the innermost core of a Neutron Star may have exotic stuff like Quark Gluon Plasma. Nothing conclusive here, but its not all Neutron at the core center.

To understand the process, please refer the table 1(a) given in the link R(s) and R(p) are tabulated. For example a stable neutron Star of around 1.7 Solar Mass has an observed/calculated radius of around 10-12 Kms, for this object R(s) = 4.9 Kms and R(p) = 7.6 Kms. Here R(s) is Schwarzschild radius and R(p) is packing radius beyond which the quarks gap will reduce and energy release would start. Now suppose this object accretes mass, its radius would reduce, nothing substantial will happen till it encounters the respective mass R(p), once it attempts to fall below R(p) [R(s) is still lower], then energy release takes place and its mass reduces. It does not mean that entire object has converted into Quark Star. What it states is that R(p) somehow acts as a mass shedding point which prevents the object from falling below R(s).

Not very complex to visualize.

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Thanks.

11. ### NotEinsteinRegistered Senior Member

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But your paper assumes neutrons only, not exotic stuff like a quark-gluon plasma. So are you saying your own paper is wrong?

12. ### NotEinsteinRegistered Senior Member

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Note: I will not be nitpicking at typo's, minor grammar mistakes, or inconsequential errors.

Paper 1:

1.1: I certainly hope this doesn't turn out to be an ad hoc addition to Pauli's Exclusion Principle...

1.2: Neutrons are not hard spheres, so the application of the Kepler Conjecture needs some discussion. Let's hope that happens later on... Additionally, the neutrons in the core of a neutral star have a lot of kinetic energy, and are superfluidic. In other words: there is no packing possible, because there is no solid.
Doesn't the radius of a neutron depend on its speed? I seem to remember that if particles are traveling at relativistic speeds, the radius becomes ill-defined, and one should use its cross-section (which is a function of speed).
But let's continue under the assumption that these neutrons are "cold"; in other words, they have negligible kinetic energies.
However, do note that one cannot use the TOV limit in this case, as the matter we are dealing with is no longer modeled by a perfect fluid.

2: We are now comparing the Schwarzschild radius to the packing limit. Since there is no mention of kinetic energies, I think we are indeed working under the assumption that we are dealing with a ball of cold, static matter. Note that in a real neutron star there is a sizable contribution to its mass from the kinetic energies, through the famous $E=mc^2$ equation.

Table 1 appears to be missing units for the radius?

I'm also missing the binding energy for the neutrons. If you pack neutrons this densely, there's going to be contributions of potential energy to the total energy that needs to be evaluated. I don't see them being discussed at all. So we are working under the assumption that the neutrons are not bound together, even though they are tightly packed, which seems quite contradictory.
"With this conclusion author proposes that a physical Neutron Star exists which is smaller than Event Horizon in size."
(Ignoring the bad grammar.) I expect there to be a discussion somewhere how such an object can be stable inside the event horizon.

End of 2.0: The functional form of the k-function in the definition of R(n) was never given, so it is impossible to verify some of the claims and numbers in Table 1. This makes the statements that neutron stars of 2.65 solar masses or more cannot form and the claim that there is still room for more neutrons in neutron star with 3.24 solar masses deserving of further attention.

2.1: The statement that connects the Heisenberg uncertainty to the relativity of neutrons is complete nonsense: they have nothing to do with each other.

2.2: No comment.

2.3: Again with the Heisenberg uncertainty vs relativistic. However, here a mistake is made: the neutrons are declared relativistic, but the kinetic energy is once again not taken into account. In other words, the largest contributor to the mass of the object is ignored!
This entire paper depends on the fact that one can pack neutrons densely (under high pressure) as if they were incompressible spheres. QFT strongly disagrees with this approach, and thus the entire paper can be dismissed because one of the primary assumptions is incorrect. On top of that, many contributions to the mass of the object have been neglected, making the calculated numbers very suspicious.

Paper 2:
Page 2: "assuming the density ($\rho$) as constant" this is wrong: such objects don't exist, and they certainly aren't neutron stars. This assumption invalidates all further results depending on it.

Page 3: "will require that the density decrease outward" exactly, but now you appear to be contradicting your own assumption!

1.3: We use the (wrong) results from the first paper.

2: All of a sudden we consider the possibility of squeezing the neutrons! That contradicts the assumptions of the first paper, and thus requires a discussion about when this squeezing happens. If it happens before the densely packet structure of the first paper forms, then this second paper disproves the conclusions of the first. However, no such discussion is in this paper; it is simply assumes to be the case.
Additionally, it's not clear one can actually squeeze neutrons this way... I expect a QCD calculation to demonstrate that when the neutrons are close enough together the gluons they start exchanging allow for the hand-wavy "squeeze" interpretation. Remember, neutrons aren't hard spheres (as this paper clearly write about, in contradiction to the first paper), and neutrons applying pressure onto each other needs QCD calculations to model.
In fact, our current understands suggests if one were to squeeze neutrons this way, one would get a quark-gluon plasma, for which the proposed tight packing obviously doesn't apply anymore.

3.1: Ah, I guess we were using kilometer as the missing unit in table 1.
Top of page 5: Again with the "not fully relativistic" statement with the wrong "as there is still room" explanation. That is not how one determines whether something is relativistic or not.
A couple of lines later there is the statement that as dX goes to zero, velocity goes to c. This appears to be related to the misinterpretation of the Heisenberg uncertainty principle?
The Buchdahl limit is mentioned: this limit is of course not applicable here, because we don't have a liquid but a solid.
Additionally, there is no calculation that the energy released in the proposed manner actually reduces the mass enough to prevent a total collapse. It is merely silently assumed to be the case.
And at the end, the claim that all incoming mass will be converted to energy in order to maintain stability at the high mass bound is of course deserving of more discussion, because this appears to violate, for example, lepton number conservation. E.g. an electron cannot be converted into pure energy, because where does its lepton quantum number go?

3.2: (i) It is stated that as the mass of the object inside the event horizon continues to be converted into energy, the Schwarzschild radius shrinks (even though the paper correctly states the energy cannot escape). This is a fundamental misunderstanding of GR, and flies in the face of $E=mc^2$. The energy inside the event horizon contributes to its mass, so a conversion from mass to energy cannot affect the Schwarzschild radius. The point made in the paper here is thus wrong.

(ii) The neutrons are called almost relativistic again, even though they are tightly packed with a low kinetic energy. Additionally, we don't have neutrons anymore, but a quark-gluon plasma.
The star is proposed to "bounce" out of its Schwarzschild radius. This is once again a misunderstanding of what an event horizon is.

(iii) A "black neutron star" has a core of energy with a shell of neutrons? Please show calculations that such a state is stable-ish for even a millisecond. And in what form does this energy exist anyway?

Conclusion: all three possibilities given are physically incorrect.

3.3: Five lines above the end of page 7, we once again have an object coming out of its Schwarzschild radius due to mass to energy conversion.

13. ### RajeshTrivediValued Senior Member

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At the outset I must thank you for going through the papers.
Its actually WIP (work in progress) and finally, I am able to associate gravity with Asymptotic Freedom.
Its admirable that you picked up above point 3.2(i), it took me huge time to get over with this aspect when I first thought of it. I will explain and hope I am correct in my reasoning.

First and foremost, I am trying to establish that an object cannot fall beneath its Schwarzschild Radius via the route of accretion by a Neutron Star. These 3.2(i), (ii) and (iii) actually consider a very rare scenario when the implosion (or collapse of the progenitor star) is so dynamic that the inner most core falls within its Schwarzschild Radius. This means a visible Neutron Star will not be present but there will be a transient object, quite similar to a Neutron Star but inside its Event Horizon. This can only happen if the core mass is > 3.24 Solar because from this mass onwards R(s) > R (p), suggesting that R(p) is encountered only after the core has fallen below its Event Horizon and collapsing. as soon as R(p) is encountered the release of energy starts, but an inner most core part of 3.24 Solar Mass (or below) can never fall below its Schwarzschild Radius**, and hence a photon generated at the center of this object can actually travel radially away from the center.

Now you are right that an observer outside the bigger object Even Horizon, will see the mass+energy unchanged, that why the outer event horizon still remains intact, but the photon released from the center and which has traveled away from the center is not influencing the inner core, there is no gravitational back pressure by the photon on the inner core. As the object continues to collapse more and more photons are generated (reduction in inner mass) which are stuck within outer most horizon but due to absence of back pressure by these photons, a stage comes when these photons no longer can remain trapped, the escape velocity falls below c and and explosion happens.

**[Pl refer to the table a core of 3.24 Solar Mass will have R(s) = R(p) = 9.5 Kms, transition point, for lower mass core R(p) > R(s), means the energy release will trigger before R(s) is encountered and hence a core smaller than 3.24 Solar Mass can never fall below its Event Horizon, incidentally that is the lower mass limit for a Black Hole.]

14. ### NotEinsteinRegistered Senior Member

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You really need to calculate this through GR. We're inside the event horizon, and geodesics can behave very strangely in this region. Your hand-wavy "traveled away from the center" doesn't cut it. For example, the lack of gravitation might be compensated by radiation pressure from the outside, caused by photons that were emitted but are bending back and hitting the object.

Without a proper consideration of the geometry of spacetime inside the event horizon, this argument isn't very strong. Additionally, conventional GR prevent anything from leaving the event horizon (ignoring Hawking radiation), and thus from the outside the mass of the black hole will never decrease. It is thus impossible for the Schwarzschild radius to shrink in the way you describe.

Let's say a photon is emitted by the object in a radial direction. It starts traveling towards the event horizon. Why does the photon never reach it? It can't hover right in front of it, because it has to travel at the speed of light. Where does this photon end up?

I've raised serious issues with the way you have calculated these numbers in my previous post; please address those too.

15. ### RajeshTrivediValued Senior Member

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Couple of issues you have raised.

1. The first aspect of my proposal is that a stable Neutron Star cannot form a BH via the route of mass accretion. The energy released in the innermost core will radiate away, thus reducing the mass and preventing falling of the object beneath its Schwarzschld radius. This is possible because R(p), the trigger point for energy release, is encountered before the R(s).

2. The second case, that is what if the core falls within its Event Horizon, but this could happen only if R(s) > R (p). You raised some points here. The energy release would start inside Event Horizon, when the core encounters R(p), at this point the structure is more or less like that of a Neutron Star, the curvature of the spacetime around (even though inside EH) is still not weirdly high, it is quite similar to that of curvature of spacetime around an ordinary visible Neutron Star. As shown in my previous posts, the innermost core (of 3.24 Solar mass or below) will not fall below its EH, so the photon would travel away till it encounters a point where escape velocity = c.. This point keeps shifting upward (still within the original object EH) as the inner mass reduces.

3. I looked around for bending of photons and creating back pressure on the surface. I could not find, can you supply a paper which talks of this back pressure by a photon? Even otherwise as I have stated the curvature is not so high as the structure is still like that of a NS, its nowhere near singularity.

4. Regarding calculations of R(s) and R(p). The R(s) is the main literature part, on the R(p) I must say that..

1. There is no harm in assuming Neutrons as rigid spheres to start with, that enables Kepler Conjecture.
2. The compressibility aspect of Neutrons and cubic (HCP crystal) formation under extreme pressure find some mention in the main literature.
3. I have taken radius of Neutron as 0.55 fm.

These three points lead to tally with TOV limit for upper mass limit of a neutron Star, any inaccuracy in radius of Neutrons or compressibility factor will delay (or shift) the R(p) only, the trigger point for release of energy, the conclusion will not change. The conclusion is valid as long as R(p) > R(s) for core greater than 1.4 solar Mass (EDP limit). With the parameters taken by me this comes out to be 3.24 Solar Mass.

16. ### NotEinsteinRegistered Senior Member

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As I said, that is impossible because there are conservation laws preventing the total conversion of various particles into pure energy. For example, the conservation of lepton number. If I throw an electron into a black hole, some of it must remain as a particle with rest mass (there are no massless leptons in the Standard Model).

The event horizon as seen from an observer infinitely far away, I presume?

Please show the calculation in GR that proves that this happens. Please show that a redistribution of energy within the event horizon can affect the event horizon radius.

I don't know whether it's there or not, but my question to you is: where do these photons go otherwise? They can't cross the event horizon, and they can't hover in place. So they must obtain a stable orbit (which is impossible inside the event horizon), or fall back down to the object.

Doesn't matter; the curvature is strong enough to create an event horizon, so the issue still stands.

Yes there is! Particles are not rigid spheres, and you are absolutely wrong about that. Neutrons are composite particles, so if you try to pack them tightly, you are going to have to deal with the strong nuclear force.

Link? But it doesn't matter, because the neutrons inside a neutron star have quite a bit of kinetic energy, so there is no "formation" to speak of. In fact, they are superfluidic, so the entire idea of densely packing them it out the window.

Without mentioning where you got this number from, I might add.

Wrong. If you assume a solid (which you have with your dense packing), the TOV limit does not apply. The TOV limit needs a perfect fluid.

17. ### RajeshTrivediValued Senior Member

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I am talking about release of (940-12=928 MeV or part thereof) quark quark bond energy. I see no violation of conservation law here. I am not at all talking about of conversion of any particle into energy.

My claim is and I have shown with the simple maths that a photon produced at r = 0, can travel radially away till it encounters a point where escape velocity is c. I am aware that in GR, once inside Event Horizon, all the directions are towards r = 0, but I do not see how GR can account for this motion of a photon produced at r = 0. I do not see any rational inaccuracy in my this claim. If there is any, you tell me pl, I am open.

This point has much more, but first let us resolve this.

I am dealing with strong Nuclear interactions, by invoking Asymptotic Freedom. Whether particles are rigid sphere or not hardly matters, as I said it just shifts the R(p) point.

Superfluid or crystalline or solid, hardly matters because the point of trigger of energy is when constituent quarks gap is reduced. That is imminent. And by the way TOV calculations under GR begs for super fluid for simplicity, its not that any equation of state is known to us which mandates us to do calculations around Super Fluid, and moreover the upper mass limit (or TOV limit) with the GR invoking is a vastly spread figure (from 1.7 to 3) suggesting poor or incomplete modelling, due to lack of understanding of EOS in the core. The idea is to find out the upper mass limit of a Neutron Star.

18. ### NotEinsteinRegistered Senior Member

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You claim that any additional matter thrown onto a neutron star at maximum mass will be completely converted into energy, which (as I have pointed out) cannot happen due to (for example) the conversation of lepton number.

This naive picture of how photons behave in the presence of (strong) gravity is not correct. Please use GR in this case, as only GR gives a proper description. The concept of escape velocity for photons is nonsensical in GR; you have to work with geodesics and such.

Then might I suggest you learn some GR? Because obviously GR accounts for it! Not a single worldline from inside the black hole can ever escape, and this includes photons produced at r = 0 in a radial direction.

Please provide your equations for the geodesic for this photon. That is the only way to deal with photons in GR.

OK

No, asymptotic freedom is only one result from QCD. You need to take all the other consequences into account. What is the bonding strength between the quarks in the neutron? How do the gluon fields react to this pressure? You have left any essential parts out. Show through calculations what kind of matter is left behind after all the energy is released.

It calls into question your dense packing idea. Please show that your dense packing formula is valid when the spheres used are not rigid.

In fact, you yourself have made them non-rigid: you can squeeze them!

As I've already told you, some of your core arguments fail when it's not a liquid, so it matters quite a bit.

You are confusing two different issues. This is about the dense packing and the usage of the TOV limit, not the energy release when squeezed.

That is not a proper response to the issue raised. The TOV limit is calculated under the assumption of a perfect fluid, meaning it cannot be used when the matter present is too different from a perfect fluid. You are applying it to a solid. That is about as different from a perfect fluid as one can get. In other words, you are applying the TOV limit when you are not allowed to. Thus all the results coming from this flawed application are immediately suspicious.

19. ### RajeshTrivediValued Senior Member

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I understood your point. I am stating that when "any additional matter is thrown onto a neutron star" its radius reduces and if this reduction in radius challenges gap between innermost quarks, then the energy releases at the innermost core. So you see the mass thrown and accumulated at the upper layers, incoming mass, is not converted. If so then you were right, it would violate many conservation law, but thats not the case here.

I do not know naive picture or otherwise, but indeed its very simple and under the aegis of known Physics. The concept of escape velocity is not "nonsensical" in Physics and as i stated the derivation of Schwarzschild radius can be done by invoking escape velocity.

And more importantly I do not understand the significance of geodesic inside the superconducting core of all Neutrons. Whatever I know of GR, it talks about geometry of spacetime around a mass not inside the mass. So, either please refer me to some literature or show me with your knowledge of GR that a photon produced at r = 0, will stay put at r = 0 only. I have shown that it can travel away.

The brief is Asymptotic Freedom only. When quarks gap is reduced to zero, both of them become free in a sense that bond strength between them becomes zero. I cannot claim (and its open research area) what constituent 940-12 = 928 MeV, I am proposing that its bond energy and it gets released when quarks are freed thus reduction in mass. I have taken 100% (928 MeV) as energy in my next step (when I associate gravity with AF), but that we can skip as of now.

What is left over is actually quarks in the innermost core. I am not right now stepping in what happens to these quarks on explosion or what is the equation of state here. That again is an open research area even under prevalent Quark Gluon Plasma consideration.

There is some miscommunication here. To move ahead I have invoked R(p) by considering certain radius for Neutrons and considering them spherical. But what R(p) signifies is the point beyond which the constituent quarks gap reduces. This is the point where Asymptotic Freedom comes into picture,bond strength reduces and energy release starts. So if there is any issue with radius of neutron or neutron compressibility then this trigger point changes, not the conclusion. I have not claimed that my R(p) calculations are precise, they are subject to my assumptions.

20. ### NotEinsteinRegistered Senior Member

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Ah, I indeed didn't realize that. In that case: prove that once a neutron star reaches this maximum mass, the process of squeezing neutrons is possible. In other words, prove that such a neutron star has the right conditions for neutrons to be squeezed.

Incorrect. Your claims are at several points fully incompatible with GR and QFT. Your claims are at best compatible with a Newtonian particle view of the world, but you are in an environment where you have to use both GR and QFT for a proper description. Because you are not doing that correctly, your description of what happens is suspicious.

Those are hand-wavy derivations that happens to give the right answer; please learn GR and the proper way to derive the Schwarzschild radius.

Wait, your photons never leave the surface of the neutron star? How does that work?

I have never claimed that.

No you haven't. You have simple stated that. I see no derivation or proof in your paper or here.

So you have no idea what else QCD says about neutrons. You cannot calculate a single thing with it. Maybe you should learn how QCD works, so you can actually calculate how much energy gets put into gluons, instead of photons? Because I have a strong suspicion (looking at the PDF's of neutrons) most energy might end up as gluons.

So you predict a collapse into a quark star. In other words, using many hand-wavy and incorrect calculations, you make a prediction real scientists have already made. How are you doing anything new?

The only new prediction you make is that the object inside the event horizon won't collapse into a black hole, but because it's inside the event horizon, and we don't have a quantum theory of gravity, that's all wild speculation, and quite irrelevant, because stellar mass black hole don't evaporate that quickly.

I don't mind you setting an effective radius for neutrons, or considering them spherical. I mind you making them rigid, solid spheres, because neutrons are most definitely not that.

Prove with a calculation that this is that point, and it doesn't happen earlier or later.

And since your assumptions and approximations are wrong, the result should be considered wrong too. Neutrons inside a neutron star don't pack densely; they form a liquid, not a solid. This invalidates your usage of the TOV limit, and your calculations of R(p). Just that alone throws most of your conclusions out the window.

Please provide an argument with calculations that show that your modeling of the superfluidic neutrons inside a neutron star, by a densely packed structure of rigid neutrons of that radius is warranted.

21. ### RajeshTrivediValued Senior Member

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At least we are through with conservation related issues.
Sqeezing or compression of Neutrons is also there in theory. As per present understanding if the mass accretes beyond the maximum mass of a Neutron Star, then it collapses to form a BH. I am differing a bit here only, my proposition is that before it could collapse below its event horizon, it encounters a point wherein quarks gap reduces, this will weaken the qq bond and energy releases and mass reduces. This prevents the object from falling beneath its event horizon. This I have been able to establish because for cores below 3.24 solar mass R(p) > R(s). You can surely question these R(p) values, but as I said the conclusion does not change.

GR and QM they do not go together. I asked you to tell me what happens to a photon produced at r = 0, either it remains there at r = 0 (you deny this) or as per my claim it travels away till it approaches a point where escape velocity is c. I do not know any third option. So either you agree with me on this or you agree that a photon stays put at r = 0. we can move ahead on this, only if you clarify your objection.

I disagree. Something which is sensible in Physics, can be irrelevant in GR but not 'nonsensical'. Escape velocity is an integral part of celestial mechanics. Calling the well established "escape velocity formula as hand-wavy derivation that happens to give right answer" is not a sound argument.

I never said that, on accretion by a neutron star, the innermost core releases energy (on encountering R(p)), which travels outward as the nature of inner core is superconducting type, and this escapes the object, thus reducing its mass.

No I am not predicting the collapse into quark star. The rest mass of constituent quarks (of a neutron) is just around 1%. My focus is on balance 99%.

As I said as long as the point at which the quarks gap reduces happens, the conclusion does not change.
Unfortunately no any mistake in neutron radius or neutron compressibility aspect or neutron EOS will shift the point, result will be unchanged.
I am not using TOV limit, I made a reference to it to bring to notice that there is a upper limit for neutron star mass.

22. ### RajeshTrivediValued Senior Member

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NotEinstein,

I am afraid it will become too repetitive now onwards, but there is one very interesting point here, I am seeking its answer under GR, please let me know.

1. Suppose an object (say of 15 Solar Mass) is inside its event horizon, just below its event horizon (around 45 kms in size).
2. At this instant a photon is produced at the center of this object.

Where will this photon go? Can it travel away from center?

I scanned the literature, it talks of all photons/particles entering event horizon (falling inside) travels towards r = 0, but nowhere motion of a photon originated at the center is discussed.

23. ### NotEinsteinRegistered Senior Member

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That is not squeezing; the neutrons may just fall apart. If I remember correctly, the temperature rises to the point where neutrons fall apart into their constituent particles, and it thus forms a quark-gluon plasma. No squeezing required.

Yes, that is your claim, but you have made no calculations to show this process is even possible in QCD.

This is neither here nor there. You are using both as well.

Well, let's see what GR has to say about the matter:
https://i.stack.imgur.com/rhk1V.jpg

In the right picture, we can clearly see that GR predicts that all photons emitted close enough to = 0 falls back to r = 0. So there's your option three.

As my above posted image shows: escape velocity is not used in GR. Perhaps I should've called it "irrelevant to the point of nonsensical to use it".

But it's not a fundamental part of GR, which is what we're talking about.

Except that it is. Using a possibly ill-defined construct even though there are descriptions available coming directly from first principles is not the right way to go about arguing for your position. Above I've provided what GR actually says about the matter, and as you can clearly see, the "escape velocity" argument doesn't do the GR-description justice.

So your statement that you do not understand the significance of geodesics inside the object was just an irrelevant statement?

But you claim all that energy is radiated away. Please describe what kind of matter is left after all that energy is radiated away, and please specifically address the different with a quark star.

So you have no calculation to show when (of even if) this happens. You are just making unfounded assumptions. Even if your answer is right, you cannot provide evidence for it.

Assuming the order of magnitude doesn't change, sure, but that's not the point.

Then I suggest you scrap section 1.2 from your second paper, as it is misleading (with the possible exception of equation 9).

Yes, I understand now that you have no GR calculations to back up your claims, you do not understand what QCD predicts, and you are using approximations that you cannot justify. If you cannot back up any of these claims, then indeed, we will not get very far.

I have coincidentally just answered this above in this post. It will travel to r = 0, but slightly in the future.

Perhaps you should study black hole dynamics, as it's quite obvious what to look for when you understand the field of study.