Does the Immirzi Parameter Determine Black Hole Entropy in Loop Quantum Gravity?

[atyy]

Apparently it cannot, as of today, give an answer this question, because one has to put it in by hand. I guess that's why many people don't take this point serious. But at least the area law seems to come out, which is encouraging because this is one of the most important features of QG.

I'm wondering from the way it's calculated, is it more like the entanglement entropy, and so more like a correction to the Bekenstein-Hawking entropy than the Bekenstein-Hawking entropy itself?

 

[Physics Monkey]

Maybe all this means that LQG is wrong and it can't even give the correct answer to the entropy of a Black Hole.

I would say that LQG is probably a consistent mathematical structure, although unlike string theory it does not have as clear a relation to what we would call classical gravity. Thus "wrong" would only mean that it doesn't describe the particular thing we call quantum gravity in our world. Nevertheless the theory may still be quite interesting/useful/stimulating and merit attention. String theory certainly has met this qualification already, even if it has nothing ultimately to do with our particular universe.

Also, I think its fair to say that LQG can give black hole entropy, it just requires a little extra information (at the current level of development). As surprised suggested, I think the area law is the tough bit, although I agree that getting the coefficient right is also important. It would be much worse for the theory if the area law had not come out or if the parameters of the theory could not be adjusted in a way consistent with the semiclassical result. Only then would I say that LQG cannot give the correct answer to black hole entropy.

 

[tom.stoer]

Let me reawaken this thread.

I know that BH entropy can be derived from LQG in agreement with Bekenstein-Hawking by fixing the Immirzi parameter to a specific value.

I know that the Imirzi parameter enters the construction of spin networks / spin foams and that there are certain "subclasses" of LQG related to some special values i, 0, 1, ∞; ...

Looking at the classical Nieh-Yan / Holst action one can start a renormalization group approach a la "asymptotic safety" taking into account the couplings κ (Newton's constant), γ (Barbero-Immirzi), Λ (cosmological constant) and others - which are hopefully driven to zero by the renormalization group flow. Here different "theories" are not distinguished by different values but by different trajectories in the γκΛ-space.

How are these different approaches related?
How does this renormalization group flow change when fermions are added?

I know that with SU(2)_q defomed spin networks Λ is related to the deformation parameter q.

How does this fit together with the renormalization group flow?

 

[tom.stoer]

push ...

 

[Demystifier]

A recent calculation suggests that the black-hole entropy in LQG does NOT depend on the Immirzi parameter:
http://xxx.lanl.gov/abs/1107.1320
More precisely, the entropy is A/4 (Bekenstein-Hawking, Immirzi independent) plus a topological Immirzi-dependent term which does not depend on the surface A.

This seems to be a very surprising result, but even more surprising is that Marcus hasn't already drawn our attention to this paper. :-)

 

[tom.stoer]

This seems to be a very surprising result, but even more surprising is that Marcus hasn't already drawn our attention to this paper. :-)

The fact that marcus has not yet commented on this paper proves its nonexistence ...

... honestly, thanks for the reference; I have to think about it ...



That would change my list slightly, but the main questions are not affected:

I know that the Imirzi parameter enters the construction of spin networks / spin foams and that there are certain "subclasses" of LQG related to some special values i, 0, 1, ∞; ...

Looking at the classical Nieh-Yan / Holst action one can start a renormalization group approach a la "asymptotic safety" taking into account the couplings κ (Newton's constant), γ (Barbero-Immirzi), Λ (cosmological constant) and others - which are hopefully driven to zero by the renormalization group flow. Here different "theories" are not distinguished by different values but by different trajectories in the γκΛ-space.

How are these different approaches related?
How does this renormalization group flow change when fermions are added?

I know that with SU(2)_q defomed spin networks Λ is related to the deformation parameter q.

How does this fit together with the renormalization group flow?

 

[marcus]

I logged the Ghosh Perez paper in the bibliography when it came out. Thanks Demy! It looks as if it could be important.

Alejandro gave an invited talk (BH Entropy and Chern-Simons) on 26 May at the Madrid Loops conference
http://loops11.iem.csic.es/loops11/index.php?option=com_content&view=article&id=184 At the very end, right before the QA, he briefly mentioned a connection between CS level and immirzi parameter.

The slides PDF and video of the talk are available. I looked at the slides and did not see these Ghosh Perez results, nor did I see reference to collaboration with Ghosh. Perhaps the paper was still in the works, so Alejandro had no reason to mention it. btw Amit Ghosh ( http://www.phys.psu.edu/people/display/?person_id=166 ) has a number of papers on BH entropy. PhD Calcutta 1997, postdoc at Penn State (among other places), visitor Marseille during May 2011, homebase at Calcutta. Someone to be aware of. The Marseille visitor list ( http://www.cpt.univ-mrs.fr/~quantumgravity/ ) gives some idea of the level of activity and collaboration.

 

[bcrowell]

As a total LQG ignoramus, it seems to me that there might be multiple possible ways of interpreting the Ghosh-Perez result. On the surface, it seems inconsistent with previous results, which claimed to be able to fix the IP. So:

(A) LQG has multiple methods for calculating entropy, they give different results, and there is no way of telling which is right, except by reference to some other theory; or
(B) Ghosh and Perez have given (or someone else can give) a clear and compelling physical explanation for why their method is right and previous methods were wrong.

If it's A, LQG has serious problems. If it's B, LQG-ers should be dancing in the streets.

Ghosh and Perez do seem to make a serious effort to tell a compelling physics story in their paper, but it's not a story whose merit I can judge with my level of (lack of) expertise.

 

[marcus]

... LQG-ers should be dancing in the streets.
...

there have been a number of indications that it would be nice if the IP were free to run.

So if the Ghosh Perez results are confirmed a lot of people will be happy.

If I'm not mistaken they show that the familiar value is recovered in a certain limit.

But the exact value of the IP is not the main thing. What they primarily do is they get the S = A/4 to fist order without the IP entering in. That is a stronger result. Before, one had to adjust something to get that equality. Now one has it plain and simple: muchmuch better.

BTW the sense that IP should run or be involved in renormalization appeared already in a 2007 paper by Ted Jacobson (major QG guru with a lot of foresight) http://arxiv.org/abs/0707.4026 made an impression on me so I've been waiting for the other shoe to drop. This could be it, and it might not. Also there may have been something by Kowalski-Glikman in the past year, but my memory of that is dim, can't be sure.

Anyway it has always been awkward that the IP appeared in S = A/4 at leading order, because that fixed it. Ghosh Perez refer to this as a kind of vulnerability. They may have cured that, freeing it up.

I hope it will be confirmed. It's exciting, as you point out. I don't know enough to offer an opinion about the validity, and how it will hold up. I have to wait and see, hoping.

 

[Demystifier]

As a total LQG ignoramus, it seems to me that there might be multiple possible ways of interpreting the Ghosh-Perez result. On the surface, it seems inconsistent with previous results, which claimed to be able to fix the IP. So:

(A) LQG has multiple methods for calculating entropy, they give different results, and there is no way of telling which is right, except by reference to some other theory; or
(B) Ghosh and Perez have given (or someone else can give) a clear and compelling physical explanation for why their method is right and previous methods were wrong.

If it's A, LQG has serious problems. If it's B, LQG-ers should be dancing in the streets.

Ghosh and Perez do seem to make a serious effort to tell a compelling physics story in their paper, but it's not a story whose merit I can judge with my level of (lack of) expertise.

I disagree with only one statement: that you are a total LQG ignoramus.

 

[marcus]

Since the last few posts have been about the new paper by Ghosh Perez, I'll copy the abstract here for reference---and note a related paper by Kowalski-Glikman.

58]http://arxiv.org/abs/1107.1320
Black hole entropy and isolated horizons thermodynamics
Amit Ghosh, Alejandro Perez
(Submitted on 7 Jul 2011)
We present a statistical mechanical calculation of the thermodynamical properties of (non rotating) isolated horizons. The introduction of Planck scale allows for the definition of an universal horizon temperature (independent of the mass of the black hole) and a well-defined notion of energy (as measured by suitable local observers) proportional to the horizon area in Planck units. The microcanonical and canonical ensembles associated with the system are introduced. Black hole entropy and other thermodynamical quantities can be consistently computed in both ensembles and results are in agreement with Hawking's semiclassical analysis for all values of the Immirzi parameter.
5 pages

My comment would be that the reason you can have a horizon temp be independent of the BH mass is that this temperature is measured by an observer hovering down near the horizon----not by somebody at infinity.

One important aspect of their result is that they get S = A/4 without having to adjust the Immirzi parameter.

So the IP is still free and may play a role in renormalization or relation to the cosmological constant. This is a big change. You used to have to adjust the IP to a fixed value in order to recover S = A/4. I noticed a hint of this back in March 2011, with a paper by Jerzy K-G and Remy Durka.

Also there may have been something by Kowalski-Glikman in the past year,...

http://arxiv.org/abs/1103.2971
Gravity as a constrained BF theory: Noether charges and Immirzi parameter
R. Durka, J. Kowalski-Glikman
(Submitted on 15 Mar 2011 (v1), last revised 30 May 2011 (this version, v2))
We derive and analyze Noether charges associated with the diffeomorphism invariance for the constrained SO(2,3) BF theory. This result generalizes the Wald approach to the case of the first order gravity with a negative cosmological constant, the Holst modification and topological terms (Nieh-Yan, Euler, and Pontryagin). We show that differentiability of the action is automatically implemented by the the structure of the constrained BF model. Finally, we calculate the AdS--Schwarzschild black hole entropy from the Noether charge and we find that, unexpectedly, it does not depend on the Immirzi parameter.
6 pages,... to be published in Physical Review D

Jerzy K-G would be familiar to many of us, but his PhD student Durka perhaps less, so here is Remy's homepage as introduction:
http://www.ift.uni.wroc.pl/~rdurka/
In like manner, people may be less familiar with Perez' co-author Amit Ghosh, so I'll repeat what I said earlier:
Amit Ghosh ( http://www.phys.psu.edu/people/display/?person_id=166 ) has a number of papers on BH entropy. PhD Calcutta 1997, postdoc at Penn State (among other places), visitor Marseille during May 2011, homebase at Calcutta... The Marseille visitor list ( http://www.cpt.univ-mrs.fr/~quantumgravity/ ) gives some idea of the level of activity and collaboration [now in progress at Marseille].

 

[Finbar]

Its perhaps good to point out that if one can show that any proposed UV completion of general relativity has the right semi-classical limit it must reproduce the Hawking-Bekenstein entropy in this limit to leading order. So the string theory calculation that recovers it was a for gone conclusion once it was shown that string theory has the right semi-classical limit.

The converse is not true though. Reproducing the Hawking-Bekenstein entropy does not ensure that the theory has the right semi-classical limit.

What this means is that the real challenge to LQG is to get the right semi-classical limit.
If the value they get for the number of microstates within some calculation is not the
HB one then this might only mean that they have not yet taken the semi-classical limit.
Somehow LQG researches need to understand how the parameters in their theory flow to the IR.

The final comment in the R. Durka, J. Kowalski-Glikman seems to agrees with me

In both cases it remains to be understood in details how the proposed mechanisms work. This question is related to the notorious problem of the semiclassical limit of Loop Quantum Gravity, and it seems that without controlling this limit one cannot make any definite conclusions.

 

[marcus]

Its perhaps good to point out that if one can show that any proposed UV completion of general relativity has the right semi-classical limit it must reproduce the Hawking-Bekenstein entropy in this limit to leading order. So the string theory calculation that recovers it was a for gone conclusion once it was shown that string theory has the right semi-classical limit.
...

I'm something of an Andy Strominger fan. I give him a lot of credit for proving S=A/4 in the special case of extremal black hole. Not a trivial result, at the time, I think.
http://arxiv.org/abs/hep-th/9601029
Microscopic Origin of the Bekenstein-Hawking Entropy
A. Strominger, C. Vafa

I suspect you know what you are talking about, though---often a lot is in how we define our terms.
=========================

However this is a bit off-topic. The topic here is the Immirzi Parameter and its role in LQG.

 

[marcus]

This thread is about the Immirzi parameter (IP) and its role in LQG and it looks like we are seeing a NEW TAKE on the Immirzi emerge, notably with this paper by Ghosh and Perez that we were discussing on the previous page:

Since the last few posts have been about the new paper by Ghosh Perez, I'll copy the abstract here for reference---and note a related paper by Kowalski-Glikman.

58]http://arxiv.org/abs/1107.1320
Black hole entropy and isolated horizons thermodynamics
Amit Ghosh, Alejandro Perez
(Submitted on 7 Jul 2011)
We present a statistical mechanical calculation of the thermodynamical properties of (non rotating) isolated horizons. The introduction of Planck scale allows for the definition of an universal horizon temperature (independent of the mass of the black hole) and a well-defined notion of energy (as measured by suitable local observers) proportional to the horizon area in Planck units. The microcanonical and canonical ensembles associated with the system are introduced. Black hole entropy and other thermodynamical quantities can be consistently computed in both ensembles and results are in agreement with Hawking's semiclassical analysis for all values of the Immirzi parameter.
5 pages

My comment would be that the reason you can have a horizon temp be independent of the BH mass is that this temperature is measured by an observer hovering down near the horizon----not by somebody at infinity.

One important aspect of their result is that they get S = A/4 without having to adjust the Immirzi parameter.

So the IP is still free and may play a role in renormalization or relation to the cosmological constant. This is a big change. You used to have to adjust the IP to a fixed value in order to recover S = A/4...

=======
I like the appearance of a chemical potential here, energy associated with spin net punctures---i.e. with increasing by one the number of links of the spin network passing through the horizon. The chemical potential µ_∞ is this potential seen by an observer at infinity. They also use a µ which is measured by a nearby observer, hovering close to the horizon. This µ is negative up to a critical value of the Immirzi, which I think is around 0.274.

So the chemical potential being negative (as long as the IP is less than its critical value) means that more punctures are favored. The system will relax by developing a spin network state which has more punctures.

This is also favored entropically.

Holding the area constant while increasing the number N of punctures means having more puncture colored with lower spins----more spin = 1/2 labels---subject to whatever constraints of geeometry, other things being equal.

It's an intriguing paper, to say the least! I think one way that this is an advance is they recognize that as defined the usual BH event horizon is unphysical. In a quantum world one does not have access to some idealized "past of future null infinity" (all the more because the thing is evaporating).
So they don't use the unphysical EH----they use the IH (isolated horizon) concept. That alone helps to make this paper different from some of its precursors. Finbar I expect you are thoroughly familiar with this, but in case others are reading, here is a reference:

http://arxiv.org/abs/gr-qc/0407042
Isolated and dynamical horizons and their applications
Abhay Ashtekar, Badri Krishnan
(Submitted on 13 Jul 2004)
Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner. In this framework, evolving black holes are modeled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity; suggested a phenomenological model for hairy black holes; provided novel techniques to extract physics from numerical simulations; and led to new laws governing the dynamics of black holes in exact general relativity.
77 pages, 12 figures. Published in Living Reviews of Relativity

 

[marcus]

From page 4 of Ghosh Perez
Classically, the only natural value of the chemical potential is zero, which implies
1 = ∑(2j + 1) exp(−2πγ√[j(j + 1)]).
(My comment: This is what determines γ_o the critical value of γ.)
Some background on the number 0.274 is here:
http://arxiv.org/abs/0906.4529
See equation (9) on page 4. A more precise value and its square root:
(0.274067...)^1/2 = 0.5235...

 

[genneth]

marcus: I just read through that old Ashtekar review paper on isolated horizons; it seems that *all* LQG calculations of entropy uses isolated horizons? Ghosh+Perez even point out that their main contribution is to introduce "quantum hair" by counting punctures of the IH --- so I don't think the use of the isolated horizon is novel here. Certainly, for a classical Schwarzschild BH (the analogue of what Ghosh+Perez looks at) the event horizon should correspond to the IH (at least classically; the former is not well-defined with hbar > 0).

 

[marcus]

Certainly, for a classical Schwarzschild BH (the analogue of what Ghosh+Perez looks at) the event horizon should correspond to the IH (at least classically; the former is not well-defined with hbar > 0).

That is a good point! The earlier papers may not have used IH---they may have used EH. But the point is that the two should correspond.

So intuitively the difference must arise elsewhere---e.g. in their keeping track of the number of punctures.

Thanks for giving this a closer look!

"...it seems that *all* LQG calculations of entropy uses isolated horizons?..."

That's not how I remember it (I can check back to the 1996-1998 papers) but your point makes the issue seem unimportant.

 

[marcus]

I fished up the March 1996 paper of Rovelli, the earliest LQG BH entropy paper I know of, and the earliest that Ghosh Perez cite. It might be interesting to take a look. (I think this was before the concept of IH was defined, but you point out this should not matter.)

http://arxiv.org/abs/gr-qc/9603063
Black Hole Entropy from Loop Quantum Gravity
Carlo Rovelli
(Submitted on 30 Mar 1996)
We argue that the statistical entropy relevant for the thermal interactions of a black hole with its surroundings is (the logarithm of) the number of quantum microstates of the hole which are distinguishable from the hole's exterior, and which correspond to a given hole's macroscopic configuration. We compute this number explicitly from first principles, for a Schwarzschild black hole, using nonperturbative quantum gravity in the loop representation. We obtain a black hole entropy proportional to the area, as in the Bekenstein-Hawking formula.
5 pages

The concept of isolated horizon was, I think, introduced in this 1999 paper:

http://arXiv.org/abs/gr-qc/9905089
Isolated Horizons: the Classical Phase Space
A. Ashtekar, A. Corichi, K. Krasnov
(Submitted on 23 May 1999)
A Hamiltonian framework is introduced to encompass non-rotating (but possibly charged) black holes that are 'isolated'' near future time-like infinity or for a finite time interval. The underlying space-times need not admit a stationary Killing field even in a neighborhood of the horizon; rather, the physical assumption is that neither matter fields nor gravitational radiation fall across the portion of the horizon under consideration. A precise notion of non-rotating isolated horizons is formulated to capture these ideas. With these boundary conditions, the gravitational action fails to be differentiable unless a boundary term is added at the horizon. The required term turns out to be precisely the Chern-Simons action for the self-dual connection. The resulting symplectic structure also acquires, in addition to the usual volume piece, a surface term which is the Chern-Simons symplectic structure. We show that these modifications affect in subtle but important ways the standard discussion of constraints, gauge and dynamics. In companion papers, this framework serves as the point of departure for quantization, a statistical mechanical calculation of black hole entropy and a derivation of laws of black hole mechanics, generalized to isolated horizons. It may also have applications in classical general relativity, particularly in the investigation of of analytic issues that arise in the numerical studies of black hole collisions.
43 pages, 2 figures

I'm not sure (you may know) but the concept of IH may have been refined subsequently. And the definition of IH emended in later papers. I haven't followed it--this is just the earliest reference I can find.

 

[thesamer]

http://arxiv.org/abs/1111.0961"
Immirzi parameter and Noether charges in first order gravity
R. Durka
(Submitted on 3 Nov 2011)
The framework of SO(3,2) constrained BF theory applied to gravity makes it possible to generalize formulas for gravitational diffeomorphic Noether charges (mass, angular momentum, and entropy). It extends Wald's approach to the case of first order gravity with a negative cosmological constant, the Holst modification and the topological terms (Nieh-Yan, Euler, and Pontryagin). Topological invariants play essential role contributing to the boundary terms in the regularization scheme for the asymptotically AdS spacetimes, so that the differentiability of the action is automatically secured. Intriguingly, it turns out that the black hole thermodynamics does not depend on the Immirzi parameter for the AdS-Schwarzschild, AdS-Kerr, and topological black holes, whereas nontrivial modification appears for the AdS-Taub-NUT spacetime.

17 pages, to appear in The Proceedings of "Quantum Theory and Symmetries 7" Prague, Journal of Physics: Conference Series (JPCS)

 

[Demystifier]

A recent calculation suggests that the black-hole entropy in LQG does NOT depend on the Immirzi parameter:
http://xxx.lanl.gov/abs/1107.1320
More precisely, the entropy is A/4 (Bekenstein-Hawking, Immirzi independent) plus a topological Immirzi-dependent term which does not depend on the surface A.

This seems to be a very surprising result, but even more surprising is that Marcus hasn't already drawn our attention to this paper. :-)

I would like to add two info about this paper.

First, it is published in Phys. Rev. Lett.
http://prl.aps.org/abstract/PRL/v107/i24/e241301

Second, today a refutation of a critique of that paper appeared:
http://xxx.lanl.gov/abs/1204.4344

 

[marcus]

A recent calculation suggests that the black-hole entropy in LQG does NOT depend on the Immirzi parameter...

More precisely, the entropy is A/4 (Bekenstein-Hawking, Immirzi independent) plus a topological Immirzi-dependent term which does not depend on the surface A.

This seems to be a very surprising result, but even more surprising is that Marcus hasn't already drawn our attention to this paper. :-)

That was the Ghosh Perez paper and I did call attention to it as soon as it came out. But I did not succeed to raise much attention by calling, that time. :-D.

You might be interested to learn of a followup paper by Frodden Ghosh Perez, that came out in October 2011. I think people are closing in on the right answer--what Loop geometry should say about BH and BH entropy in particular. My hunch is that it is going to turn out that to first order there will be no dependence of S on Immirzi.

Maybe Ghosh Perez result is not right but my hunch is it is in the right direction. Just have to wait and see.
Here is the more recent Frodden Ghosh Perez paper:
http://arxiv.org/abs/1110.4055

 

[marcus]

A calculation posted on arxiv today indicates that in Loop gravity black hole entropy
S = A/4 in general to first order and as suggested earlier does not depend on the Immirzi parameter.

Some earlier posts on this thread from back around July 2011 discussed this possibility.

Today's paper represents the first time the coefficient 1/4 has been derived in general in any type of quantum gravity. (String theory results are for very special "extremal" black holes, not what one expects to find in nature.) So if confirmed, as I expect it will be, this is a landmark paper.

There are situations in Loop gravity when one may want the Immirzi to run with scale, so it's nice not to have it nailed down to one fixed specific value. Ted Jacobson already suggested the desirability of this back in the 2007 as I recall, in a paper about LQG black holes.

So this seems to be coming about. http://arxiv.org/abs/1204.5122
Entropy of Non-Extremal Black Holes from Loop Gravity
Eugenio Bianchi
(Submitted on 23 Apr 2012)
We compute the entropy of non-extremal black holes using the quantum dynamics of Loop Gravity. The horizon entropy is finite, scales linearly with the area A, and reproduces the Bekenstein-Hawking expression S = A/4 with the one-fourth coefficient for all values of the Immirzi parameter. The near-horizon geometry of a non-extremal black hole - as seen by a stationary observer - is described by a Rindler horizon. We introduce the notion of a quantum Rindler horizon in the framework of Loop Gravity. The system is described by a quantum surface and the dynamics is generated by the boost Hamiltonion of Lorentzian Spinfoams. We show that the expectation value of the boost Hamiltonian reproduces the local horizon energy of Frodden, Ghosh and Perez. We study the coupling of the geometry of the quantum horizon to a two-level system and show that it thermalizes to the local Unruh temperature. The derived values of the energy and the temperature allow one to compute the thermodynamic entropy of the quantum horizon. The relation with the Spinfoam partition function is discussed.
6 pages, 1 figure

Maybe there is no connection with Jacobson's earlier paper here, really. It just reminded me of it. Jacobson's paper hit my funnybone and I made one or two speculative comments about it when it came out:
https://www.physicsforums.com/showthread.php?t=178710
http://arxiv.org/abs/0707.4026
Renormalization and black hole entropy in Loop Quantum Gravity
Ted Jacobson
7 pages
(Submitted on 26 Jul 2007)

"Microscopic state counting for a black hole in Loop Quantum Gravity yields a result proportional to horizon area, and inversely proportional to Newton's constant and the Immirzi parameter. It is argued here that before this result can be compared to the Bekenstein-Hawking entropy of a macroscopic black hole, the scale dependence of both Newton's constant and the area must be accounted for. The two entropies could then agree for any value of the Immirzi parameter, if a certain renormalization property holds."

Jacobson's reference [15] is a Martin Reuter paper
[15] M. Reuter and J. M. Schwindt, “Scale-dependent metric and causal
structures in quantum Einstein gravity,” JHEP 0701, 049 (2007)
[arXiv:hep-th/0611294].

Ah! I see that Bianchi already made the connection and referred to Jacobson's 2007 paper in his conclusions section--as reference [20].

 

[atyy]

A calculation posted on arxiv today indicates that in Loop gravity black hole entropy
S = A/4 in general to first order and as suggested earlier does not depend on the Immirzi parameter.

Some earlier posts on this thread from back around July 2011 discussed this possibility.

Today's paper represents the first time the coefficient 1/4 has been derived in general in any type of quantum gravity. (String theory results are for very special "extremal" black holes, not what one expects to find in nature.) So if confirmed, as I expect it will be, this is a landmark paper.

There are situations in Loop gravity when one may want the Immirzi to run with scale, so it's nice not to have it nailed down to one fixed specific value. Ted Jacobson already suggested the desirability of this back in the 2007 as I recall, in a paper about LQG black holes.

So this seems to be coming about.


http://arxiv.org/abs/1204.5122
Entropy of Non-Extremal Black Holes from Loop Gravity
Eugenio Bianchi
(Submitted on 23 Apr 2012)
We compute the entropy of non-extremal black holes using the quantum dynamics of Loop Gravity. The horizon entropy is finite, scales linearly with the area A, and reproduces the Bekenstein-Hawking expression S = A/4 with the one-fourth coefficient for all values of the Immirzi parameter. The near-horizon geometry of a non-extremal black hole - as seen by a stationary observer - is described by a Rindler horizon. We introduce the notion of a quantum Rindler horizon in the framework of Loop Gravity. The system is described by a quantum surface and the dynamics is generated by the boost Hamiltonion of Lorentzian Spinfoams. We show that the expectation value of the boost Hamiltonian reproduces the local horizon energy of Frodden, Ghosh and Perez. We study the coupling of the geometry of the quantum horizon to a two-level system and show that it thermalizes to the local Unruh temperature. The derived values of the energy and the temperature allow one to compute the thermodynamic entropy of the quantum horizon. The relation with the Spinfoam partition function is discussed.
6 pages, 1 figure

Maybe there is no connection with Jacobson's earlier paper here, really. It just reminded me of it. Jacobson's paper hit my funnybone and I made one or two speculative comments about it when it came out:
https://www.physicsforums.com/showthread.php?t=178710
http://arxiv.org/abs/0707.4026
Renormalization and black hole entropy in Loop Quantum Gravity
Ted Jacobson
7 pages
(Submitted on 26 Jul 2007)

"Microscopic state counting for a black hole in Loop Quantum Gravity yields a result proportional to horizon area, and inversely proportional to Newton's constant and the Immirzi parameter. It is argued here that before this result can be compared to the Bekenstein-Hawking entropy of a macroscopic black hole, the scale dependence of both Newton's constant and the area must be accounted for. The two entropies could then agree for any value of the Immirzi parameter, if a certain renormalization property holds."

Jacobson's reference [15] is a Martin Reuter paper
[15] M. Reuter and J. M. Schwindt, “Scale-dependent metric and causal
structures in quantum Einstein gravity,” JHEP 0701, 049 (2007)
[arXiv:hep-th/0611294].

Ah! I see that Bianchi already made the connection and referred to Jacobson's 2007 paper in his conclusions section--as reference [20].

From the section on p5, "partition function and spin foams", isn't this a semi-classical calculation?

 

[Demystifier]

In view of these new papers, what exactly is wrong with older papers which calculate entropy to be Immirzi-dependent?

 

[Physics Monkey]

I too would like to know if any more understanding is available.

I still have some elementary confusions/reservations. For example, looking at Eq. 2 in http://xxx.lanl.gov/pdf/1107.1320v3.pdf it looks to me like the authors have written $S = S_{BH} + S_q$ with $S_q$ almost defined so that $S_{BH}$ is the right semiclassical answer. I don't doubt that the proposal has more content than this, but to the extent that N is proportional to A, then the full entropy is proportional to A and has IP dependence. Is their proposal that the semiclasssical answer gets the entropy wrong by an extensive amount? I also don't know how this connects up with the Bianchi work.

 

[Demystifier]

Perhaps we shall not have a good answer to that question until Rovelli writes a paper on it, because Rovelli seems to be the only guy in the LQG community able to write a paper truly understandable to a wider physics community.