Asymptotic Freedom in QCD and...

At a fundamental level, they are.

You have so far failed to even reply to many of the points I raised, so this is a misrepresentation of the truth.

When the object has an unrealistic constant density.

When the core of the object is not too dense.

Because "potential energy" is not fundamental in GR, and the Kruskal diagram demonstrates that a particle traveling from the EH will always be traveling towards the center of the object.

No, I'm basing my dismissal of point 3 on the Kruskal diagram. Separately from that, I'm pointing out to you that the concept of escape velocity doesn't work well in GR, and gravitational potential energy is even more hopeless.

Inward pressure is not gravitational potential energy.

That's because there is no strong gravity, so Newtonian gravity is an acceptable approximation. And in Newtonian gravity, escape velocity is a well-defined thing.

I am not the one making the arguments, you are. I'm merely pointing out the oversights in them.

I've already addressed this multiple times. But even then: if I'm wrong, then why can't you prove me wrong? Why can't you demonstrate that escape velocity is something that's well-defined and useful in the presence of strong gravity? Even my "hand waving" (and I'm obviously not) is stronger than your absence of any argument.

 

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No, that's incorrect. Pt#1 in the quote is true for the entire range of density from arbitrarily small value to very high nuclear level density.
I thought you had understood this after post #107. I will attempt again.
The density of an object of mass M, under uniformity assumption, when 'just at EH' is dependent on (c^6)/(G^3*M^2), this can be any value depending on M and need not be constant. Keeping this aspect in mind if you refer to my post#107, you will come to conclusion that pt#1 in quote is true for almost the entire range of density.

This again is incorrect. As shown above for any density value when the object is at its EH, the inner fractions will not be under their respective EHs, so a photon can at least attempt to move away till it encounters the point wherein it falls beneath the EH.

(For Neutron Star) Please calculate the value of inward gravitational pressure in GR without invoking gravitational force or gravitational potential energy. Pl show any reference which shows gravity countering NDP, without invoking these concepts.

So, please give quantitative value, beyond which escape velocity becomes well defined thing.
I am sure you will understand that approximation cannot create a new set of "now applicable" parameters. For example as you are saying PE and escape velocity is not there in GR, then your invoking these parameters in "approximation of GR" is not justifiable. Approximation gives you mathematical simplification, it does not give you new set of physical parameters.

No, there is no absence of argument from my side. It is just that you are not able to cross the bar, and repeating "its not there" argument.

1. Take for example in GR perspective, the earth is moving in a straightline around the sun, but it never leaves the sun. How can it be made to leave the sun to infinity?

2. Again in GR perspective, a bullet is fired upward with some momentum from earth's (or say even Neutron star's, so that you do not invoke weak gravity argument), it falls back. How much momentum should we impart to this bullet so that it does not fall back and goes to infinity.

[These are well defined issues in Physics, so please respond in GR without hand waving, this will give you an idea that the concept of escape velocity or binding energy is fundamental to Physics, so making a claim that it is not fundamental or irrelevant or meaningless in GR is your choice of words.]

 

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Right here you assume constant density, which is an unrealistic proposition for stellar objects. In fact, neutron stars specifically do not follow this density distribution.

The same problem exists in post #107: you assume a uniform density, which a neutron star doesn't have. The calculation that I did in post #100 (because you were unable/unwilling to) does indeed show that it is possible to have the event horizon on the outer surface of such an object, but it also signals such an object is unstable (any addition to the mass, and the entire thing starts collapsing), which is problematic, because that will happen very quickly. And it's up to you to show that neutron stars have a uniform density.

That is for a constant density value, which is not generally the case for celestial objects.

Look, if you want to start discussing this non-existent uniform density object, that's fine, but I thought you were talking about neutron stars.

https://en.wikipedia.org/wiki/Hydrostatic_equilibrium#Derivation_from_general_relativity
Done!​

Why? How is this related to what I told you? What would this add?

When GR reduces to Newtonian gravity: https://en.wikipedia.org/wiki/Newtonian_limit
Following the source: https://arxiv.org/pdf/gr-qc/9712019.pdf Equation 4.10 and 4.13
This is basic GR stuff; if you're working with event horizons, you should know this.

They are not parameters, but even if they were, your argument doesn't follow. GUT falls apart into several separate theories, each with their own parameters, but some of these can be expressed in GUT-parameters. In other words: the approximated theories contain parameters that are fully described by the full GUT. But here, they are not even parameters, there are values/variables. Under the Newtonian limit these variables work well enough to use them. In fact, you can derive this by starting with GR, taking the Newtonian limit, deriving Newton's laws of motion, and then proving that the escape velocity follows from that.

So under the Newtonian limit, escape velocity is well-defined.

And you haven't shown it to be there, not even once.

Simple. Start with a good metric, and derive the equations of motion of a stable orbit:
https://en.wikipedia.org/wiki/Schwarzschild_geodesics#Orbits_of_test_particles

Now my relativistic orbital mechanics aren't too good, but I think you'll find that as you increase the specific relative angular momentum, so does the radius of the orbit.

Why do I have to do your homework? Actually, I don't have to do it either, I just have to look it up:
http://astro.cornell.edu/academics/courses/a290/lectures/A2290_36 (Free Fall).pdf
Up to and including slide 11. A particle escaping to infinity is simply the reverse process of a particle falling in (since we have no time-dependent in our metric). So just calculate what velocity the infalling particle would have at the coordinates where you fired the bullet, and that's your escape velocity.

But see how it depends on the metric, many calculations, etc.? It's not fundamental in GR at all!

I have done as you asked. Will you now please also do as I asked?

Wrong, as I have been saying, it does exactly the opposite.

I've just shown (you know, with proof) that they are indeed not fundamental. I've never claimed that they are irrelevant or meaningless in general; they are only useful (relevant, meaningful) in specific circumstances, such as environments where the Newtonian limit is a good approximation.

Now, please show me your answers to your questions, where you demonstrate that I'm wrong about all of this.

 

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NotEinstein,

This thread has been moved to pseudoscience and I think rightly so, because more or less it has become word game, despite my best efforts.
I cannot match your sound capability in word games.

 

Hadn't noticed. But you think word games are pseudoscience? If word games were really the reason of the move, wouldn't this thread have ended up in the cesspool, or locked? Wouldn't we/I/anybody have received a mod-warning or infraction? Funny, it's almost as if nobody misbehaved (that badly), but that the thread was judged based on the merit of the ideas contained within it...

If you had been using the terminology of GR, there would have been no "word game".​

May I suggest you put some of that effort into learning GR (calculations and terminology) instead?

And apparently, you also cannot match my sound capability in GR, which is a lot more important when you think about it.

Also nice to note that you do not even attempt to address the issues I just brought up with your point #1 and #2.

 

Your objection is that my assumption of uniform density for concluding that an object just at EH, will have inner fractional parts out of their respective schwarzschild radius, is bad. Your defense is that, that is a very particular case and not applicable to celestial objects.

So let us see:
(I am not giving the calculation steps, if you find problem in deriving this density, then please let me know, I will provide the steps.)

Your objection and your implied claim that inner fractions will also be beneath their respective schwarzschild radius in general will be true only if density profile of the object follows:

d(r) > c^2/(8piGr^2)

(It is actually greater than or equal to) d(r) is the radial density at r radius.

on putting values of c and G, the above density profile becomes:

d(r) > (5.3 * 10^25)/r^2 kg/m3.

Need I elaborate further how unrealistic this density profile is?

No more word games please, because it is apparent that the moderator who shifted this thread to pseudo gave value to your apparently incorrect stand. As a critic you have good writing style, but quality is missing.

 

It is shifted to pseudo for the simple reason that you are claiming that GR is incorrect and substituting some idea that contravenes the first edict...Once the Schwarzchild radius is reached an EH is formed and what we know as a BH is formed...Professor Link Barnard had the same problem getting you to understand similar mainstream edicts.....the boys at "Cosmoquest" told you repeatedly the problems that existed that prevented any legitimacy in your hypotheticals, along with of course two or three warnings re your own hand waving, refusal to answer all questions and general obtuseness.

 

What is a "radial density"? Is it the same as \(\rho(r)\)?

I'd like to see the calculation, because I don't trust your resulting formula. For one, there's a factor of 3 difference between your and my result. Additionally, I'm very interested how you have performed the integration of the density distribution.

You should take issues you have with the moderation up with the administrators. And if you think I'm playing word games (on purpose), take up that issue with the moderators.

And GR calculations are missing from yours, so quality is missing there as well.

 

Simple thing for you would be to show how my formula is incorrect and off by a factor of 3. If you could do that fine otherwise please retract your claim

Even otherwise let us say it is off by 3, the resultant density profile becomes > 1.59 * 10^26/r^2 kg/m3. Please show that this is the realistic density profile for a celestial object just at its EH.

The point is very simple, as long as density profile is < (5.3 * 10^25)/r^2, the inner fractional mass will not be inside the respective EH (when the total mass is just at EH). And in general when the celestial object (collapsing star core etc) is just at its EH, the maximum density is of the order of nuclear density (10^17 kg/m3) much less than the values calculated. Density is much more rarer for higher mass cores at EH. So realistically speaking, my proposal that when an object is just at its EH, the inner fractions will not be beneath their respective EHs, is good. Hope you get it this time in totality.

[For simplicity I have taken the uniform density profile, any realistic density profile, which surely will be rarer than 5.3*10^25/r^2, will give the same conclusion]. Do you agree or not?

 

Was it Prof Link "Barnard" ?
You have not gotten the gist of my proposal as yet. My stand is that when the core is "just at its EH" not yet fully collapsed to form the singularity), then a photon produced at any inner point (especially at or near the center) can travel upward. This is the first step, because so far it was mistakenly understood that every path is towards r = 0. [Which is true once the singularity is formed, but not true when the object is just at its EH and collapsing]. This is conclusively proved in my post#107 and #129.

The second step would be to take this photon out (again before the singularity is formed), this may or may not create any conflict with GR.

The thread does not deserve to be in pseudo, because it talks of established concepts, but then that I leave on people who decide.

 

Of course it does! and will continue to deserve to be where it is as long as you keep claiming your nonsense as some sought of fact. eg: Once Shcwarzchild radius is reached, the EH is created and subsequently a BH from which nothing gets back out by crossing that same EH.
That's what you were told over at Cosmoquest and what Professor Bennett Link also told you.

 

You really want me to compare the two formula's? Alright then.

Post #100: I give:
\(\rho\leq\frac{3c^2}{8G\pi r^2}\)

Post #126: You give:
\(d(r)\leq\frac{c^2}{8\pi Gr^2}\)

Assuming that my \(\rho\) is the same as your \(d\) (you've ignored that question), the only difference between the two formula's is a factor 3.

Note that I never claimed yours was wrong; all I said was that our formulae were different, and that because I have a derivation showing and you haven't pointed out any mistakes in it, I suspect your derivation is different (for example, using different assumptions).

I'll get back to this once I understand where that number is coming from exactly (i.e., once you give the derivation). But here's a Fermi-style estimate: neutron star densities are typically in the order of \(10^{17}\) kg/m3, they have a radius of 10 km (both from: https://en.wikipedia.org/wiki/Neutron_star)
The \(r^2\) at the outer edge of a neutron star becomes a factor of \(10^{10}\) when expressed in meters. The requires density thus becomes \(10^{16}\) kg/m3, lower than the average density of a stable neutron star. Thus, it's not outside the realm of possibilities for a celestial object to reach such densities.

I will comment on this once I understand where your numbers are coming from.

Wait, you are using a uniform density profile? They are unrealistic for celestial objects, so the formula doesn't apply immediately to them. Your hand-wavy "which surely will be rarer" is not a justification to do so. I cannot tell (yet) if I agree with your conclusions or not, but I certainly do not agree with your argumentation towards those conclusions.

 

Pl refer your post#100 again. The oversight on your part is that you are using M/Volume= density, which will give you erroneous result for variable density profile. If you do the proper integration the factor 3 will go away. Even otherwise as I said in #129, this factor 3 will hardly change the conclusion as highlighted by me.

 

Nice to see the correction.

 

Well obviously! I even explicitly state I'm using a constant/uniform density. Please re-read my post #100 more carefully.

I'm asking you again: please provide those calculations. It seems that we both start from the same assumption, but get different results. That obviously isn't possible, and thus at least one of us is wrong.

It's not the factor 3 itself that worries me: it's that there is any difference. If we both start at the same starting point, we must get the same answers. We don't get the same answers, so unless one of us has made a mistake in the derivations, we are not starting at the same starting point. If you are using different assumptions that I am, it's vitally important to the discussion at hand to get those differences out in the open.

 

Appears to be a dishonest attempt. You are fooling none.
My post#129 replies to your persistent pestering about uniform density assumption of mine; you raise the objection about the density formula and then claim that you don't trust my calculations as your figures in #100 gives a value higher by a factor of 3. If that formula of yours in #100 is for uniform density, then please do not use the same for countering my#129 which is about variable density. Why don't you refer to some standard text on variable radial density - mass calculations and see for yourself that there is nothing wrong in the calculations.

No more word games pl, substantiate your claim that a density profile of the order of >10^25/r^2 kg/m3 will be of a realistic object when just at EH.

 

If you think I'm being dishonest (on purpose), feel free to get the moderators involved.

Yes, because celestial object don't typically have a uniform/constant density, so you have to show your assumption is warranted. I've told you this countless times now.

How can I trust your calculations if I can't check them, and I get a different answer? I'm not saying I trust my calculations, but now I can't even compare them to see where this difference is coming from.

Why do you refuse to give the calculations you explicitly stated you would post if I requested them?

Please re-re-read my post#100: it's clearly stated that it is.

Fro post #129: "For simplicity I have taken the uniform density profile" you have thus NOT used a variable density. Please stop contradicting yourself. Did you use a uniform/constant density, or not?

Why don't you post the calculations you said you would post?

I never claimed that. You are the one claiming celestial object with a constant density exist. You are the one building objects with event horizons on their outer surface only. Why should I need to provide evidence for your claims?

 

I refuse to get entangled with you on your word games. Its quite apparent that you are acting dishonestly, but that does not matter much to me.
Coming to your claim, which will expose your lies:

1. I proposed that under uniform density assumption when a core of mass M is "just at its EH" the inner fraction (xM where 0<x<1) will not be beneath xM schwarzschild radius.

2. You objected to my uniform density assumption, and made a claim that my statement is true only for some specific case of highly dense constant density object.

3. So, I provided you the calculations (first in #107 and later in #129) that my proposed conclusion will be untrue only if the non-uniform density profile is such that it is > 10^25/r^2 kg /m3.

4. For all other uniform or non uniform density if the density profile is < 10^25/r^2 kg/m3, my proposition is true and your objection is false and baseless word game.

5. You still persisted, so I asked you to give an example of a celestial object having density profile > 10^25/r^2 kg/m3....which will make your objection valid, you abandon your claim!


Don't you see your lies?

Please be a responsible critic, if pointed out, do not take shelter in posts here and there, acknowledge that your objection was misplaced.

 

Again, if you think I'm dishonest or lying, please get the moderators involved.

I fully agree, as per my post #100.

Yes, as it's unrealistic for celestial objects.

I don't remember doing that? Please point out where I did this.

You didn't provide the calculations, you only provided the results. I've been asking you almost every post now to actually provide the calculations!

As I said multiple times: I can only comment after I've seen the calculations!

As I said multiple times: I can only comment after I've seen the calculations!​

#1: We are in agreement on this.
#2: I don't remember doing that.
#3: I haven't commented on that (yet).
#4: I haven't commented on that (yet).

So no, I don't see my lies.

Please be a responsible person, and post the calculations you promised you would post.

 

I promised you that I would post if you cannot figure that out. But you started with a pompous claim that you cannot trust my calculations as the same is off by a factor of 3 as compared to yours. Even when I pointed out that this factor of 3 is due to your using M/V, you did not get the hint. I also stated that it does not really matter as the factor of 3 will make it > 1.5 X 10^26/r^2 kg/m3 which is even more unrealistic, but you continued with your strawman.

Ok, here is the proof: use dm = 4*pi*r^2 d(r) dr, with a condition that r < 2Gm/c^2 for every r and mass (m) contained in that r.