# Asymptotic Freedom in QCD and...

Discussion in 'Pseudoscience' started by RajeshTrivedi, Sep 14, 2017.

1. ### RajeshTrivediValued Senior Member

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So, do you agree that as long as density of any inner shell (when the object is just at EH) of radius r is < 5.3*10^25/r^2, all the inner points shall be out of their respective EHs?

3. ### NotEinsteinValued Senior Member

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The task is to find an object that has an event horizon internally, but we have to avoid hitting this condition for any radius: d(r) > 5.3*10^25/r^2

Imagine an object with a radius larger than 1 meter. We're going to focus on the core up to 1 meter, and we're going to check whether there's an event horizon there. In other words, we are going to check whether $r_s$ is larger than 1 meter at an $r$ of 1 meter.

Let's calculate the mass of this core, by assuming it's right on the edge; in other words, all throughout the core the condition is met exactly. Now, writing out the maths is boring and silly-error prone, so we're going to be lazy and use one of Wolfram Alpha's widgets, the Spherical Integral Calculator:
http://www.wolframalpha.com/widgets/view.jsp?id=89c969c21b169fa996f899d9b2a98588

Let's put in the density condition: (5.3*10^25)/(rho^2) (in mathematics, they often use rho instead of r)
And integrate rho from 0.000001 to 1, phi from 0 to 2pi, and theta from 0 to pi (just look at: https://en.wikipedia.org/wiki/Spher..._and_differentiation_in_spherical_coordinates under "Thus, for example, a function...").

Result: 1.05*10^33 (kg)

This is the mass of the core; in other words, this is the maximum possible mass of an object of 1 meter that can still meet the condition.

To check whether this object has an event horizon, we calculate its Schwarzschild radius:
$r_s=\frac{2GM}{c^2}$

This gives:
$r_s=1.485*10^-27\times1.05*10^33=1.6*10^6$ (in meters)

Since $1.6*10^6>1$, we have $r_s>r$, and thus there's an event horizon around this object.

Note that we're missing the mass up to 0.000001 meter, because there's an infinity hiding there, so there's even more room for adding mass to this object.

Conclusion: something must have gone wrong in the derivation of the density condition, because there are objects possible that meet the condition while violating what it should stand for.

In other words: obviously I do not agree, no.

5. ### RajeshTrivediValued Senior Member

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Appears incorrect.
please apply proper conditions, from r = 0 to r = 1 meter and recalculate the mass of such sphere. Please give steps how you arrived at this mass from the given density profile. Because if I apply the formula used by me then the mass of a one meter sphere with such density profile comes at = 6.7 * 10^26 kg, and Rs of such object is also 1 meter; exactly tallying.

Does not satisfy the condition.
Now assuming that your calculation is ok then also the object's Rs = 1600 km while object is of 1 meter size, that means it is not "just at EH", so you are failing the "just at EH" condition.

You will, once you understand it.

7. ### RajeshTrivediValued Senior Member

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The point of argument is drifting, which is not so relevant here, the qualitative statement is as below:

1. In general when a celestial object is just of its Schwarzschild radius, then only the outer surface is just at its EH, all other inner layer points will be out of their respective (inner shell) schwarzschild radius.

2. As the object falls deeply beneath its EH, more and more layers fall inside their respective shell EH.

3. This is simply because the mass relationship with schwarzschild radius and actual radius varies with r and r^3 respectively.

Point#1 permits us to conclude that a photon emitted somewhere inside such core (when it is just at EH), can travel in any direction, it is not a compulsion that it will travel only towards the center. So somehow if we can generate photons at or around center of the core due to some mechanism, then these photons can travel away from the center towards outer surface (for how long and how much distance, not yet ascertained, that is the next step). However as long as the object is inside its EH, this photon cannot escape to the universe.

8. ### NotEinsteinValued Senior Member

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1,496
I put it in the calculator I linked, and this is the answer I got. If you claim it's incorrect, please explain to me what kind of mistake the calculator made.

Exactly my point. It satisfies your condition on the density, but it doesn't satisfy your claim that such a density will be "just at EH", thus proving your derivation of that density to be faulty.

I can only, once you point out the supposed problem with the calculator.

Except where the object generates two event horizons; one at its core, and one on its outer surface. This is of course easy to see: take an object that's fully underneath its event horizon, and add to it a spherical shell (radius outside the core's event horizon) that is heavy enough to generate its own event horizon.
(And before you complain; I'm still waiting for the (mathematical) description of a "realistic" density distribution you claim that needs to be used.)

Agreed.

Not sure how that follows?

Probably true.

Very true.

9. ### RajeshTrivediValued Senior Member

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Please show that for such object the density of any shell of size r will not exceed 5.3*10^25/r^2.

10. ### RajeshTrivediValued Senior Member

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So, you agree that it is probable, fine, thanks.
Now give an example when it is "false" without exceeding the density beyond 5.3*10^25/r^2 kg/m^3.

11. ### NotEinsteinValued Senior Member

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Irrelevant, as you said "In general", which means your condition need not apply.

Under the assumption that you have an object where only the outer regions are within the event horizon, yes. I don't agree with the argumentation and derivation of point #1 (see above), but if you have such a situation, then photons in the inner parts of the object can probably travel somewhat outwards.

Again irrelevant, as you said "in general" in your point #1.

12. ### RajeshTrivediValued Senior Member

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So you cannot give an example? You object for the sake of objecting and when confronted, instead of backing out, you weave stories around your objections. Quite a dishonest chap you are!

My stand from the word go is very clear that as long as the density is less than 5.3*10^25/r^2 for inner shells of r (when an object is just at EH), all the inner points will be out of their respective EHs. You have not been able to counter it.

13. ### NotEinsteinValued Senior Member

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I have given an example in post #205.

It’s you who’s dismissing my objections without addressing them properly. It’s you that dodging my objections. It’s you how apparently cannot back down when proven wrong.

If you believe that, feel free to report me to the moderation staff.

I have given an example in post #205; an example that you have not been able to counter so far.

14. ### NotEinsteinValued Senior Member

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It appears that RajeshTrivedi has abandoned his/her attempts to defend his/her position?

15. ### Xelasnave.1947Valued Senior Member

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I do hope Rajesh is ok it is not like him to abandon something.
Alex

16. ### NotEinsteinValued Senior Member

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Indeed, but perhaps I'm simply impatient. It is the time of year for close friends and family, and I doubt the Sciforums crowd can compete with those.

17. ### RajeshTrivediValued Senior Member

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Actually I lost interest in this poster NotEinstein word manipulations.
He started playing with the words, almost trollish behaviour, offering no worthwhile argument.

Stay happy, healthy and prosper in new year 2018!!

18. ### NotEinsteinValued Senior Member

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As I thought: RajeshTrivedi is unable or unwilling to substantiate his/her claims, and unable or unwilling to disprove my objections. I guess everybody can draw their own conclusions.

19. ### Xelasnave.1947Valued Senior Member

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Thank you and may I wish the same for you.
Keep going if you have time all interaction should be seen as beneficial.
Alex

20. ### Xelasnave.1947Valued Senior Member

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I think perhaps your earlier observation re the time of year will prove correct.
And may I also wish you a happy and prosperous 2018.
Alex

21. ### NotEinsteinValued Senior Member

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1,496
I have to admit, it wasn't my observation originally (in another thread), so I deserve no credit there. But seeing the accusatory reply RajeshTrivedi just made, I highly doubt (s)he will continue conversering with me. Well, his/her loss!

And the same to you!