# Black hole entropy, curved space and monsters

1. Jun 25, 2007

### jal

http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.3239v1.pdf [Broken]
Black hole entropy, curved space and monsters
Stephen D. H. Hsu and David Reeb
21 June 2007
Almost all of the entropy of a given black hole must result from a smaller black hole which has absorbed some additional mass.

It is also worth noting that a single s-wave mode with energy m = 1/R = 1/M has entropy O(1), so satisfies S = Mm. Thus, a black hole can move along the S = A curve by absorbing such modes. This is arguably the smallest amount of energy that can be absorbed by the hole, since otherwise the Compton wavelength of the mode is much larger than the horizon itself.
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What is he saying?
How would the Compton wavelength fit in with the ultraviolet and an infrared cutoff, if the cut off is as a result of the minimum length and the resulting structure?
The smallest black hole has got to be bigger than the smallest wavelength that can exist.

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We seem to have some possible length scales from
http://arxiv.org/PS_cache/hep-ph/pdf/0205/0205054v1.pdf [Broken]
INSTANTONS AND BARYON DYNAMICS
DMITRI DIAKONOV
06 may 2002
The average size of instantons found in ref. 11 is ¯_ ≈ 0.36 fm and their average separation is ¯R = (N/V )−1 4 ≈ 0.89 fm. Similar results have been obtained by other lattice groups using various techniques. A decade earlier the basic characteristics of the instanton ensemble were obtained analytically from the Feynman variational principle 12,13 and expressed through the only dimensional parameter _ one has in QCD: ¯_ ≈ 0.48/_MS ≃ 0.35 fm, ¯R ≈ 1.35/_MS ≃ 0.95 fm, if one uses _MS = 280MeV as it follows from the DIS data.
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We seem to be having some possible structures from
http://arxiv.org/PS_cache/hep-ph/pdf/0608/0608197v1.pdf
Nuclear matter in the chiral quark soliton model with vector mesons
(Dated: March 22, 2007)
The idea of investigating dense nuclear matter in the topological soliton models has been developed over decades. It was first applied for the nuclear matter system with the skyrmion centered cubic (CC) crystal by Klebanov [1]. This configuration was studied further by W¨ust, Brown and Jackson to estimate the baryon density and discuss the phase transition between nuclear matter and quark matter [2]. Goldhabor and Manton found a new configuration, body-centered cubic (BCC) of half-skyrmions in a higher density regime [3]. The face centered cubic (FCC) and BCC lattice were studied by Castillejo et al. [4] and the phase transitions between those configurations were investigated by Kugler and Shtrikman [5]. Recently, the idea of using crystallized skyrmions to study nuclear matter was revived by Park, Min, Rho and Vento with the introduction of the Atiyah-Manton multi-soliton ansatz in a unit cell [6].

The chiral quark soliton model (CQSM) can be interpreted as the soliton bag model including not only valence quarks but also the vacuum sea quark polarization effects explicitly [16, 17, 18, 19]. The model provides correct observables of a nucleon such as mass, electromagnetic value, spin carried by quarks, parton distributions and octet, decuplet SU(3) baryon spectra [20, 21].
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Also, Simone Speziale is proposing a 3d double tetra as a spinfoam structure
http://arxiv.org/PS_cache/arxiv/pdf/...706.1534v1.pdf [Broken]
Coupling gauge theory to spinfoam 3d quantum gravity
Simone Speziale
June 11, 2007
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I have already figured out (my blog) the smallest black hole would consist of 6 instantons and each would be limited to moving to 3 position. The smallest black hole would consist of 24 units. (S=A/4). Also, the smallest black hole can only grow by absorbing even numbers of quantas of energy. Odd numbers and fractions are not permitted.
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From the above information I would be tempted to say that we could observe mini black holes at CERN.

What is going on? Is the logic faulty? Is spinfoam doomed?
jal

Last edited by a moderator: May 2, 2017
2. Jun 26, 2007

### jal

It’s interesting that if we were to use .36 fm, (the average size of instantons found in ref. 11 is ¯_ ≈ 0.36 fm and their average separation is ¯R = (N/V )−1 4 ≈ 0.89 fm., and the BI parameter 2.763953198, https://www.physicsforums.com/blogs/jal-58039/mini-black-holes-945/ [Broken] ,
we would get 2.763953198 * .36 = 1.0 fm which is the size of proton.

Would this mean that the smallest possible black hole would be the size of a proton?
This would make sense with the statements by Stephen D. H. Hsu and David Reeb
jal

Last edited by a moderator: May 2, 2017
3. Jun 28, 2007

### jal

I found something else that might be interesting.
http://arxiv.org/PS_cache/physics/pdf/0611/0611143v1.pdf
Holographic Views of the World
On the Occasion of Gerard ’t Hooft’s 60th Birthday
15 Nov 2006

So let’s go back to our undergraduate period (around 1997, just before the discovery of
AdS/CFT correspondence). We can quite easily reconstruct some of Gerard’s first remarks to us concerning quantum black holes.
• Black holes of the Planck scale should be indistinguishable from elementary particles.
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That seems to be pretty indistinguishable.

Diameter...Area sphere......Area circle … # quantas ….. Area ratio c/s (S)
2.763953198.....24 .............. 6 ..................... 6 ……………. ¼ …………. 1.0 fm
5.5279064....... 96 ............. 24 ................... 24 ………………. ¼ …… 1.99 fm
11.55812.........84 ............. 96 .....................96 …………… ¼ ….. 4.16 fm

If we go to the next two stable sizes of black holes with .36 fm we get 1.99 fm and 4.16 fm
Do those two numbers relate to something that you can recognize?
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jal

Last edited by a moderator: May 2, 2017
4. Jun 28, 2007

### Jim Kata

5. Jun 28, 2007

### marcus

Steve Hsu has a blog, Jal.
It's one of my very favorites among blogs
(but I'm not a bloghound so I only read it occasionally)

It's called "Information Processing"
http://infoproc.blogspot.com/

He has started a thread of discussion of this paper, so anyone interested in the paper (which provides the title and initial topic of Jal's thread here) might want to check it out. At present I see there is only one comment. Well, maybe more will show up.
http://infoproc.blogspot.com/#6467861204422704607

Last edited by a moderator: May 2, 2017
6. Jun 28, 2007

### jal

Jim Kata!
Thanks for the act of love... that is the only way that I can improve my learning.

From http://arxiv.org/PS_cache/gr-qc/pdf/0609/0609024v3.pdf
Observation of Incipient Black Holes and the Information Loss Problem
Tanmay Vachaspati and Dejan Stojkovic
07 june 2007

I can see that there is still a lot to learn about black holes.
Could you help me by explaining Appendix A and B? Does it conflict with my approach or with what Stephen D. H. Hsu and David Reeb said?
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Marcus.... Maybe Stephen will join the discussion
jal

7. Jun 28, 2007

### marcus

He may likely not come here to discuss, but anyone can go to his blog and ask a question about the paper. He'd probably welcome a chance to talk about it (only one comment so far)