# A question of string v.s LQG derivation of BH entropy -

1. Mar 23, 2007

### ensabah6

One question I have for LQG's derivation of BH entropy is this:

would any arbitrarily enclosed sphere in space, whether it's that of the surface of planet earth, or the moon, or the sun, not to mention BH's also have the same BH entropy since as I understand the calculation, it is merely counting spin network microstates on the surface of a black hole, but couldn't this also apply to any enclosed sphere? I understand that it is not volume extensive entropy but only surface entropy.

As for string theory, is the computation of bh entropy include the volume of the BH? Why hasn't it been able to reproduce Hawking results for ordinary astrophysical BH's if string theory is indeed a theory of QG.

2. Mar 24, 2007

### william donnelly

The derivation of black hole entropy I know in LQG is the one by Ashtekar, Baez, Corichi, Krasnov (http://arxiv.org/abs/gr-qc/9710007) [Broken]. Their derivation applies to "isolated horizons", which are essentially black holes in equilibrium. This constraint is applied at the classical level and causes some simplification that allows them to count the horizon states. I believe that most subsequent work is based on this approach.

In fact, I don't think any existing derivation of black hole entropy in LQG would apply to arbitrary horizons, let alone any enclosed sphere. But I would very much like to be proven wrong on this point.

Last edited by a moderator: May 2, 2017
3. Mar 24, 2007

### josh1

Youve got it backwards. Its string theory and not lqg that has been able to produce the black hole area-entropy relation. In fact, Its only string theory that has been successful in this regard. All lqg has been able to do is produce the proportionality between entropy and area, but not the correct constant of proportionality of 1/4, and it is the latter that presents the real challenge for any quantum theory of gravity. This is just one of many reasons why hardly anyone in the physics community takes lqg seriously. If you really want to understand whats going on in high energy theory, learn string theory and learn it from string theorists and not lqg people.

4. Mar 24, 2007

### ensabah6

The original papers in string theory was only in the special case of extremel BH, which do not exist in reality. The results are protected by SUSY. The results have been extended to near-extremel BH, but I am not aware that they have been generalized to all BH's.

5. Mar 24, 2007

### josh1

You've failed to appreciate the significance of this, which is that this result must be produced for any black hole solution in string theory or any other theory of quantum gravity, whether or not the solution is that of an ordinary astrophysical black hole. If string theory hadnt been able to produce the correct result, even if it is for unrealistic black holes, it would be inconsistent with the most important clue to quantum gravity we have. Like all other tests of consistency string theory has ever been subjected to, it passed this test with flying colors. The same cannot be said of any other competing theory of quantum gravity including lqg.

6. Mar 26, 2007

### Demystifier

LQG predicts that entropy of ANY surface (not necessarily a surface of an isolated horizon) is proportional to the surface. The constant of proportionality is always the same, and can be adjusted so that it agrees with that in semiclassical gravity. However, LQG does not provide any new explanation of why entropy of a black hole should coincide with that of its surface.

String theory really explains why entropy of the black hole is proportional to its surface. Quantitatively, the constant of proportionality can be calculated explicitly only in some special (unrealistic) cases, but there are qualitative arguments for proportionality with the surface even in the general case.

7. Mar 26, 2007

### william donnelly

Demystifier, could you give a url for the calculation of black hole entropy that does not depend on the isolated horizon constraints? The papers I have read on the arxiv all rely on the isolated horizon constraint, including those from this year.

8. Mar 26, 2007

### marcus

I had the same question as W.D. So I will just repeat for emphasis

Corichi has a recent series of papers on LQG BH entropy including one this year. There have been developments. Corichi also has a monograph in preparation on that topic. Nothing I've seen over the years corresponds to Demy.'s assertion as far as I can remember. So I think Demy. owes us a url. (would be interesting to have :-))

Last edited: Mar 26, 2007
9. Mar 26, 2007

### josh1

But this demonstration is a near-trivial result of the way that spin networks include degrees of freedom called links which by definition measure area.

A rather nontrivial example is the way that the entropy of highly excited strings is area-extensive. This is the string-black hole correspondence principle due to susskind. This is another one of many important clues string theory is giving us about black hole holography.

The whole game is to produce the correct factor of 1/4. If a theory cant do so, its wrong. What lqg needs is new physical input that fixes the immirzi parameter to produce the correct value. Not a single attempt has met with anything but utter failure.

The thing is that - and this is very important - lqg is a very simple theory and seems to offer no additional theoretical elbow room where such new physics could lurk. Precisely the opposite is the case with string theory.

It doesnt provide any explanation, new or old.

Well, it offers clues anyway.

The idea is to embed black hole physics in string theory by invoking the geometry of d-brane solutions with event horizons and then to use our knowledge of the spectrum of physical states of d-branes to explcitly count the number of states and compare the result to the area of the event horizon. However, this is not really an explanation of black hole holography, but it is no doubt an important clue.

10. Mar 27, 2007

### Demystifier

William Donnelly and Marcus, see the derivation of black-hole entropy in the book "Quantum Gravity" of Rovelli. This book was also available online on the Rovelli's home page, but I do not know if this is still the case. I have not been reading the corresponding original papers of Rovelli, but I pressume that the same derivation can be seen there. The idea is very simple. The entropy of a surface is essentially the number of the degrees of freedom associated with the surface, so it is hardly surprising that the result is proportional with the surface (at least when the surface is much larger than the Planck surface).

Last edited: Mar 27, 2007
11. Mar 27, 2007

### Sauron

I have been reading the derivation of black hole entropy in string theory and there are a few aspects that I don´t see clear.

For example, the problem of uniquines. You can, as has explained josh, make somethin which resembles a black hole using a few kinds of d-branes and F-strings, ok. And you can count the number of states using CFT, o.k.

But, how can you be sure that there are not diferent ways to make the same black hole with another kind of branes/strings configuratiosn. If so the number of microstates would increase (Maybe there is some uniquines theorem anyway and simply I don´t know it).

12. Mar 27, 2007

### marcus

Demy, I have the book in hardcopy and back in 2003 used to read it online. Great book! but I would not consult it for BH entropy, there has been quite a bit written since Jan 2004 when Rovelli's text went to the publisher.

I could be wrong but I think if you check out 2006 and 2007 papers by Corichi (and references therein) you will be doing yourself a favor (if you are at all interested in LQG and BH entropy.)

It is certainly NOT the case that in LQG the entropy is simply proportional to the eventhorizon area! and the relation to area seems to depend somewhat on the size of the BH.

Corichi is preparing a review article on this. A lot has been written. The review article is not yet available but you should check out his recent papers in arxiv. Hope this helps

13. Mar 27, 2007

### josh1

As a principled person who always argues honestly based on the facts as I understand them, I would only have included the exclamation mark if I believed I understood precisely what lqg does say about the area-entropy relation and was prepared to make my case in detail. You should note that one of the posting guidelines in PF requires members to back up their claims when asked and ignoring such requests when they are reasonable - especially when they do so on a regular basis - is a definite no no here. So please explain this strangely vague statement and enlighten us.

14. Mar 27, 2007

### josh1

Yes, the entropy of a particular black hole may always be viewed as counting all of the ways it couldve been made. But by a black hole we mean a particular solution of the theory. If a black hole involves different ingredients, the solution and hence the black hole - including the way its degrees of freedom are counted - will be different.

15. Mar 27, 2007

### william donnelly

Do you have a reference for this argument? Specifically, why should the logarithm of the number of ways a black hole could have formed be the same as the entropy of the thermal state as seen by an observer outside the black hole?

I understand the statistical mechanical definition of entropy, I just don't see how "ways a black hole could be made" are the same thing as "black hole microstates".

16. Mar 27, 2007

### josh1

Ive come across this way of saying things a number of times, but only in the context of black holes, but I dont have a reference. But it`s not meant in a literal way. As you know, a microstate is a collection of excitations that represent one possible configuration of a system. We then think in terms of "building" the system out of the excitations of a particular microstate with the complete collection of all possible micrsostate then representing in this sense the "different ways of building" the system.

Last edited by a moderator: Mar 27, 2007
17. Mar 28, 2007

### Demystifier

Marcus, could you specify what exactly is wrong with the simple analysis presented by Rovelli in his book? The fact that later other people made a more complicated analysis does not convince me that the earlier simpler analysis is wrong. Can you explain, in simple terms, in what sense the later results represent an improvement?

In my opinion, scientific papers are often too polite, in the sense that they often hesitate to say explicitly what are the drawbacks of earlier papers on that subject. For that reason you can understand the point of a new paper only if you already studied all earlier papers on that subject.

18. Mar 28, 2007

### marcus

Yes! But maybe this politeness has a good reason.
Remember that this is an area of expertise of Corichi---maybe he has the best judgment. He was one of the authors of the original 1997 paper Asht. Baez Corichi Krasnov, and of those four he is the only one who is currently working on it.

Moreover he is writing a review of the whole LQG/BH entropy subject.

Corichi has chosen not to directly attack earlier work and point out its limitations in an obvious way. I would understand if you think it "too polite". But maybe he is behaving with correct amount of politeness.

This business has been going on for 10 years. There have been gradual refinements. There is still room for people to disagree.

Where I personally stand (as an observer, not researcher) is not so important but I will tell you frankly that at first I was dubious of Corichi's work and gradually I am finding it more and more convincing. Partly this is because of the work by Ghosh and Mitra around the same time (2005) which seems to corroborate Corichi. Partly it is the fact that he is using computer models and brute force. I have a lot of respect for brute force number crunching as an alternative to theoretical/analytical----both are fallible so one should try to do both as a check on each other.

The Indians, Ghosh and Mitra, are very analytical, so Corichi numerical approach complements theirs.

Corichi is a prominent organizer of the Loops '07 international LQG conference this summer in Morelia. I am sure that this summer's conference will have a lot about BH!

Probably the earlier work of ten years back should be honored and quietly improved on

19. Mar 28, 2007

### josh1

Hi marcus,

You posted the following:

I think that the site guidelines (not to mention considerations of simple respect of other members) obligate you to respond in some meaningful way to the following question posted by Demystifier:

Last edited by a moderator: Mar 28, 2007
20. Mar 28, 2007

### william donnelly

I can't speak for Marcus, but I find the Krasnov/Rovelli approach to black hole entropy a little circular. They start by assuming the area is the only relevant macroscopic quantity for the black hole and so count the number of states for a fixed area. This quantity must be a function of the area by definition.