# Asymptotic Freedom in QCD and...

All noise, no quality at all.
Please refrain from insults; it's against the forum rules.

I checked few other threads and shocked to see how you trolled Schmelzer,

he also had to give up on you.
No, that "on you" is incorrect. Schmelzer couldn't defend his position (just like you can't), so he gave up. Period.

You even just short of boasted
I did no such thing. I pointed out to Schmelzer that his boasting was unwarranted, as he didn't have a clue how many peer-reviewed papers I have published. In other words, his argument of authority might back-fire in a spectacular way, so I warned him not to make one in the first place.

that you may have some peer reviewed papers published in your name, while questioning his paper as decade old with few citations, why not come forward and say what you have.
Why should I make an argument of authority? Please respond to the contents of my posts, not to the poster of them.

This thread doubly proves (along with Schmelzer thread) that you have no basic knowledge of maths
Erm, it's you that's making high school math mistakes.

and physics
Erm, it's you that doesn't even know the basics of GR or QCD.

and just trolling around.

Actually, I don't think you have any intend to do just that. Wouldn't that make your constant "intimidating" a form of trolling too?

let us take few example,

3 Solar Mass object just at EH:
Rs = 8905 Meters.
d = 2.02 * 10^18 kg/m3
Rs (of 90% core) = 8015 Meters
R (of 90% core) = 8598 Meters.

So R(90% of core) > Rs (of 90% core), Suggesting that inner 90% fraction is out of inner fraction EH.

Density calculations when the core was just of its EH size and not yet collapsed to form BH, and calculations are done for inner fraction 90%, but any fraction can be considered and will give the same conclusion.

10 Solar Mass object just at EH:
Rs = 29685 Meters.
d = 1.82 * 10^17 kg/m3
Rs (of 90% core) = 26719 Meters
R (of 90% core) = 28661 Meters.

So R(90% of core) > Rs (of 90% core), Suggesting that inner 90% fraction is out of inner fraction EH.

30 Solar Mass object just at EH:
Rs = 89056 Meters.
d = 2.02 * 10^16 kg/m3
Rs (of 90% core) = 80150 Meters
R (of 90% core) = 85983 Meters.

So R(90% of core) > Rs (of 90% core), Suggesting that inner 90% fraction is out of inner fraction EH.
You can show specific hand-picked examples all you like; if the underlying formulas are incorrect (as I've shown), you're not proving anything.

None of these density profiles are unrealistically dense or whatever as NE is handwaving, they are nuclear level or rarer.
All these clearly prove that inner fractions will be out of their respective Schwarzschild radius, this calculation is done with uniform density, I call upon this poster NotEinstein to come forward and give his non uniform density profile (within < 5.3*10^25/r^2) to disprove this, or if he has some civility he should retract his objection.
OK, that's easy. Let's take your first example, and modify it a bit:
d = 0 kg/m3 if r < 1 meter
d = 2.02 * 10^18 kg/m3 if r > 1 meter
It's non-uniform, and the numbers for Rs (of 90% core) and R (of 90% core) doesn't change significantly. However, within r < 1 meter, dm/dr = 0, in direct contradiction to your result of: dm/dr > c^2/2G. In other words, there are density profiles for which your equations do not hold.

In general (not exception) when an "object is just at EH", except the outer surface points all other inner points will be out of their respective schwarzschild radius. This condition will be false only for very high unrealistic density profiles.
You've got that first part the wrong way around: in general, your results are incorrect; they are only valid for certain density profiles. However, you still haven't been able to produce the conditions to which such density profiles must conform, as I asked you to, so nobody knows whether there are realistic density profiles for which your derivation also doesn't hold.

Additionally, since the derivation is mathematically wrong, any conclusion that you reach being right is purely accidental, as I've explained earlier.

OK, that's easy. Let's take your first example, and modify it a bit:
d = 0 kg/m3 if r < 1 meter
d = 2.02 * 10^18 kg/m3 if r > 1 meter
It's non-uniform, and the numbers for Rs (of 90% core) and R (of 90% core) doesn't change significantly. However, within r < 1 meter, dm/dr = 0, in direct contradiction to your result of: dm/dr > c^2/2G. In other words, there are density profiles for which your equations do not hold.

There are few problems in your counter which further prove your ignorance of the subject.

1. My first example is of 3 Solar Mass contained in around 9 Kms radius sphere. And you want to modify it such that r < 1 meter is empty!! Is it realistic?? How is that possible that 1 meter size vacuum is holding 3 solar mass?

2. In general the density is higher as we move towards center from the surface, you are making density d = 0 near the the center and very high density (2.02 X 10^18 kg/m3) outside. Realistic?

3. You forgot the condition, the condition which I used was if m > rc^2/2G, then only dm/dr > c^2/2G. What are you using? m = 0 for the inner r <1 meter. Is 0 < rc^2/2G?

4. Finally, this is somewhat complex for you, when we derive some density profile, our first target is to derive a profile which is continuous and differentiable for the range under consideration. Your example is just the fabricated discontinuous nonsense, that too not applicable as the condition is not satisfied.

And please learn that 3, 10 & 30 solar mass are not some hand picked examples. For your information 3 Solar is generally considered to be the minimum mass of a steller BH; 10 Solar Mass and 30 Solar Mass BHs were recently considered in GW detections. And of course you are at liberty to take 1 billion solar mass and try again. Neither the proof nor the conclusion will change.

There are few problems in your counter which further prove your ignorance of the subject.
At least one of us is indeed being ignorant here. I'd say even willfully so!

1. My first example is of 3 Solar Mass contained in around 9 Kms radius sphere. And you want to modify it such that r < 1 meter is empty!! Is it realistic?? How is that possible that 1 meter size vacuum is holding 3 solar mass?
Irrelevant. The maths don't demand realistic density distributions (and neither did you in your request). I have shown that there exists at least one density distribution where your maths are wrong, without violating any of the conditions that the density distribution must adhere to.

Yes, this density distribution is unrealistic in reality. But it still proves your maths to be wrong, or at the very least, to be incomplete.

2. In general the density is higher as we move towards center from the surface, you are making density d = 0 near the the center and very high density (2.02 X 10^18 kg/m3) outside. Realistic?
This is the same point as point #1.

3. You forgot the condition, the condition which I used was if m > rc^2/2G, then only dm/dr > c^2/2G.
This condition is not listed in post #171, which is the post we are talking about right now. You can't willy-nilly introduce new conditions; that's moving the goalposts.

What are you using? m = 0 for the inner r <1 meter. Is 0 < rc^2/2G?
I assume that last bit contains a typo?

4. Finally, this is somewhat complex for you, when we derive some density profile, our first target is to derive a profile which is continuous and differentiable for the range under consideration.
Another previously unstated condition! And this condition is obviously wrong. I haven't had the chance to mention this before, but your density profile has a big problem: it extends into infinity. In other words, your density profile does not have an edge, and your object is infinite in size. And if you add a border/edge, at the border/edge the density distribution will not be continuous or differentiable. Your demand that is must be is unjustified, and you yourself have already violated it in previous posts.

Your example is just the fabricated discontinuous nonsense,
Perhaps you should read some physics textbooks: pretty much all density distributions used in them are "discontinuous nonsense". In fact, even heard of "point particles"; they are even worse!

that too not applicable as the condition is not satisfied.
(The grammar is broken.)
You mean the condition you just introduced?

And please learn that 3, 10 & 30 solar mass are not some hand picked examples. For your information 3 Solar is generally considered to be the minimum mass of a steller BH; 10 Solar Mass and 30 Solar Mass BHs were recently considered in GW detections.
Right, as I said, some hand picked examples. Personally, I'd rather keep using variables, as they are much more broadly applicable.

And of course you are at liberty to take 1 billion solar mass and try again. Neither the proof nor the conclusion will change.
Right, because your derivation will still be wrong.

But let's check out that condition: $$m>\frac{rc^2}{2G}$$

The Schwarzschild radius is given by:
$$r_s=\frac{2Gm}{c^2}$$

Combining the two, we get:
$$r_s>\frac{2G}{c^2}\frac{rc^2}{2G}$$

Simplifying:
$$r_s>r$$

In other words, we're below the event horizon. If this condition is to hold for all points in space, you've just constructed a universe that's just one big black hole, everywhere. You call that realistic?

Irrelevant. The maths don't demand realistic density distributions (and neither did you in your request). I have shown that there exists at least one density distribution where your maths are wrong, without violating any of the conditions that the density distribution must adhere to.
Yes, this density distribution is unrealistic in reality. But it still proves your maths to be wrong, or at the very least, to be incomplete.
This condition is not listed in post #171, which is the post we are talking about right now. You can't willy-nilly introduce new conditions; that's moving the goalposts.

Another dishonest attempt. Both the realistic aspect of the density distribution and the condition (m>rc^2/2G) are explicitly stated in my post#144. You have started lying now?

copy of my post#144 showing the condition and realistic aspect in bold (color).
Rajesh Trivedi said:
Ok, once more;

What are you countering : My argument and
My argument is that when an object is just at its EH, the inner fractions will not be beneath their respective EHs.

1. In my post#107, I proved that my conclusion is good for uniform density.
2. In my post#129, I proved that my conclusion is good for non-uniform realistic density profiles.

For my conclusion to be false, for non uniform density profiles,

rs > r (for all the shells of various r from 0 - outer EH.)

Where 'r' is the radius of some arbitrary inner fractional sphere of mass m (when the bigger object is at EH) and rs is the schwarzschild radius of this inner shell of radius r.

this will give:

2Gm/c^2 > r
m > rc^2/2G
dm/dr > c^2/2G
4*pi*r^2*d(r) > c^2/2G
d(r) > c^2/(8*pi*G*r^2)
d(r) > (5.3 * 10^25)/r^2

(is it realistic density profile?? If yes, pl show, if no then my conclusion prevails and retract your objection.)

What's your problem with this derivation?

You are changing the goalpost by taking shelter in some funny density profiles (1 meter vacuum holding 3 solar mass) and dishonestly accusing me that I did not talk about realistic density profiles. Let see what you come up with in your next post. Some more lies or word games?

Another dishonest attempt.

Both the realistic aspect of the density distribution and the condition (m>rc^2/2G) are explicitly stated in my post#144.
Sure, although you haven't quantified what "realistic" really means. But that's neither here nor there, because I was working off of post #171. Are you saying that post is wrong?

You have started lying now?

copy of my post#144 showing the condition and realistic aspect in bold (color).
So post #171 is wrong?

You are changing the goalpost by taking shelter in some funny density profiles (1 meter vacuum holding 3 solar mass)
Please look up what "changing the goalpost" means.

Any "funny" density profile that conforms to the set conditions, but leads to an incorrect or nonsensical conclusion disproves the validity of your derivation.

and dishonestly accusing me that I did not talk about realistic density profiles.
Please point me to the part of post #171 where you are raise the condition that the density profiles have to be realistic. And while you're at it, please define it mathematically.

Let see what you come up with in your next post. Some more lies or word games?

Here's a fun one: take UY Scuti, probably the largest star currently known. It has a radius of about 1700(!) times the sun. Plug that into your formula, d(r) > c^2/(8*pi*G*r^2). I get a number less than 40 kg/m3 at its outer surface. In other words, throw a big stone at this star, and you've created an event horizon at its surface! Does that seem "realistic" to you?

Here's a fun one: take UY Scuti, probably the largest star currently known. It has a radius of about 1700(!) times the sun. Plug that into your formula, d(r) > c^2/(8*pi*G*r^2). I get a number less than 40 kg/m3 at its outer surface. In other words, throw a big stone at this star, and you've created an event horizon at its surface! Does that seem "realistic" to you?

Again deliberate misrepresentation.
I said when the object is "just at EH", that means for your fun star UY Scuty (Mass around 10 Solar mass, taking the higher estimate), when it is collapsed to roughly 30 Km radius (assuming mass remains intact, which is highly unlikely). Now plug the numbers into the formula and see what you get.

Keep reading #144 again and again till you understand that its contents are absolutely correct. Take help.

End of Discussion;

Again deliberate misrepresentation.

I said when the object is "just at EH",
Those words are not in post #171?

that means for your fun star UY Scuty (Mass around 10 Solar mass, taking the higher estimate), when it is collapsed to roughly 30 Km radius (assuming mass remains intact, which is highly unlikely). Now plug the numbers into the formula and see what you get.
I think I figured out what's happening. Let's take a look at the opening sentence of post #171:
"For any given spherical object (not reduced to BH singulairty), all the points including interior points will lie on respective Event Horizon (an interior point respective EH is by considering the mass inner to this point), then to satisfy this condition,"

I think I'm getting confused by the broken grammar. I think you meant:
"For any given spherical object (not reduced to BH singulairty), when all the points including interior points will lie on respective Event Horizon (an interior point respective EH is by considering the mass inner to this point), then they to satisfy this condition,"
(Proposed additions underlined, with removals in red.)

Instead of you claiming that for any given spherical object, all points will lie on their event horizon, you mean: for any object for which all interior points lie on their event horizon, that condition applies. So post #171 is about very specific objects, not just any old (neutron) star out there. Got it, sorry for the confusion.

Keep reading #144 again and again till you understand that its contents are absolutely correct.
Could you at the very least address the issues raised in post #143? Which you started doing, but then we got sidetracked after post #150.

Take help.
What's that supposed to mean?

End of Discussion;
Yes, end of the discussion about post #171. Let's get back on track with addressing the issues in post #144!

What the hell are we supposed to understand from "assuming its mass remains intact" ??

Of course it's intact, it's still a mass density, it doesn't vanish or something.

What the hell are we supposed to understand from "assuming its mass remains intact" ??

Of course it's intact, it's still a mass density, it doesn't vanish or something.

It doesn't .

It's just mathematical dancing .

Mathamatics of physics has symbols and each symbol represents a thing and interaction and consequence therefo .

The key is to remmeber what these numbers mean . And In the sub-text of the coefficient .

Once you memorize these symbols . ( tough to do really ) .

The challenge becomes when you change the equation(s) and imagine or through experiment , understand the consequences , by the change in the equation(s) .

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What the hell are we supposed to understand from "assuming its mass remains intact" ??

Of course it's intact, it's still a mass density, it doesn't vanish or something.

A 30 solar star of this radius, is not going to remain a 30 solar, when it comes to a stage of collapse due to fusion process becoming endothermic (after Fe formation in the core).

NotEinstein is giving a wild example of an object which is far too big as compared to its EH, while I am talking about a very specific situation when object is just of its EH size or just below.

RajeshTrivedi: Can I take your lack of a response to my points in post #189 as you refusing to defend your claims?

RajeshTrivedi: Can I take your lack of a response to my points in post #189 as you refusing to defend your claims?

I am sorry but you are dishonest in your argument.
First you accused me of "willy nilly introducing new condition" which i did not, my stand is consistent throughout, then you accused me of not talking about realistic density profiles, that too when I am consistently talking about realistic density profiles (#129 or #144 etc), just because you did not see the word realistic in #171 you made a false claim that I was not. It is you, who is not here and not there, giving some vague and unrealistic objections. (like 1 meter vacuum countering few solar mass, then some square function, then some inverse function, then some parallel line, UY Scuti.....all irrelevant arguments, none of these are connected with the basic premises that is "object just at its EH".).

I would suggest, go back to #144, that is absolutely correct for the "given scenario" and sums up my argument, but still if you have any valid objection, put it down without invoking any vague nonsense like your 1 meter vacuum object. Till then pl stop claiming that you have proved something relevant.

I am sorry but you are dishonest in your argument.

First you accused me of "willy nilly introducing new condition" which i did not, my stand is consistent throughout,
In post #168, I warned that "you are making assumptions/imposing restrictions without naming them. Please also post these additional assumptions/restrictions." And then, in post #171, you summarized your argument, leaving out critical assumption/restrictions/conditions. That's why I got confused: I asked you to prove a complete version of your argument, and then you provide a version of your argument that's even more incomplete then before.

then you accused me of not talking about realistic density profiles,
A uniform density profile is indeed not realistic for celestial objects.

that too when I am consistently talking about realistic density profiles (#129 or #144 etc),
That was referring to the uniform density profiles you have been using. But let's take a look at the density profile in post #144: "d(r) > (5.3 * 10^25)/r^2" It's not actually a density profile, but a condition places on the density profile. Immediately obvious is that there's infinite density at r = 0, thus creating a singularity. Additionally, I don't think you've listed any celestial object that can manage such densities (I gave some examples of objects that can reach it in outer regions), so please explain to me how that density profile is realistic?

just because you did not see the word realistic in #171 you made a false claim that I was not.
"you are making assumptions/imposing restrictions without naming them. Please also post these additional assumptions/restrictions."
Using the word "realistic" without defining it in any way is a very underhanded way of introducing conditions/restrictions, especially right after I asked you explicitly to list the conditions/restrictions in a clear way.

It is you, who is not here and not there, giving some vague and unrealistic objections. (like 1 meter vacuum countering few solar mass, then some square function, then some inverse function, then some parallel line, UY Scuti.....all irrelevant arguments, none of these are connected with the basic premises that is "object just at its EH".).
Yes, your math cannot survive those situations, thus proving your derivations are incorrect. That's how maths work: you claim your math is correct, I only have to find a single situations that complies with the conditions/restrictions set to disprove the entire thing.

I would suggest, go back to #144, that is absolutely correct for the "given scenario" and sums up my argument, but still if you have any valid objection, put it down without invoking any vague nonsense like your 1 meter vacuum object. Till then pl stop claiming that you have proved something relevant.
Actually, no need for me to write a new post: you haven't addresses many of the issues raised in post #145 and #148 yet, so those are still waiting for you.

But let's take a look at the density profile in post #144: "d(r) > (5.3 * 10^25)/r^2" It's not actually a density profile, but a condition places on the density profile. Immediately obvious is that there's infinite density at r = 0, thus creating a singularity. Additionally, I don't think you've listed any celestial object that can manage such densities (I gave some examples of objects that can reach it in outer regions), so please explain to me how that density profile is realistic?

Yes, it is indeed a condition, but for what?
It is quite clear that you are not aware what you are objecting.

Yes, it is indeed a condition, but for what?
It is quite clear that you are not aware what you are objecting.
It's the requirement on an infinitely-sized spherically symmetric object, where all of its interior is beneath the event horizon. Which is a silly thing and unrealistic thing to even be talking about.

That was referring to the uniform density profiles you have been using. But let's take a look at the density profile in post #144: "d(r) > (5.3 * 10^25)/r^2" It's not actually a density profile, but a condition places on the density profile. Immediately obvious is that there's infinite density at r = 0, thus creating a singularity. Additionally, I don't think you've listed any celestial object that can manage such densities (I gave some examples of objects that can reach it in outer regions), so please explain to me how that density profile is realistic?

It's the requirement on an infinitely-sized spherically symmetric object, where all of its interior is beneath the event horizon. Which is a silly thing and unrealistic thing to even be talking about.

It gives me an impression that you do not know what you are objecting.

My point of view is:
"That when an object is just at its EH, then all other interior points shall be out of their respective EHs. This statement will be false only if the density of inner shell of radius r is > 5.3 * 10^25/r^2, which appears unrealistic. So whether it is uniform density or non uniform density, if it does not exceed above value, then my point of view stands."

Now tell me clearly, without unnecessary words, what is your objection.

It gives me an impression that you do not know what you are objecting.

My point of view is:
"That when an object is just at its EH, then all other interior points shall be out of their respective EHs. This statement will be false only if the density of inner shell of radius r is > 5.3 * 10^25/r^2, which appears unrealistic. So whether it is uniform density or non uniform density, if it does not exceed above value, then my point of view stands."

Now tell me clearly, without unnecessary words, what is your objection.
This is trivially proven wrong. At r = 0, create a super-heavy mass. Your condition at r = 0 evaluates to infinity, meaning this super-heavy mass doesn't meet your condition of d(r) > 5.3 * 10^25/r^2. But, I can make it arbitrarily heavy, as long as I don't make it (unphysically) infinitely heavy. I can certainly make it heavy enough to generate an event horizon at small r, while still having an event horizon at the outer surface too. Conclusion: your condition is not enough to enforce that there only is an event horizon at the outer surface of the object.