# LQG black hole model

I am currently working myself into black hole physics and I am interested in their possible quantum geometric description by means of LQG.

Can anybody please tell me good sources to start with? Since black holes were studied in this framework for a longer time, what is the most recent status?

On top, I have the following problem: With my superficial understanding I am puzzled by the fact that the quantum states of the LQG black hole are supposed to be distinguishable from each other. How does this come about? In most quantum physical problems the objects are supposed to be indistinguishable.

atyy
In most quantum physical problems the objects are supposed to be indistinguishable.

In quantum mechanics, two electrons are identical and indistinguishable. This results in a symmetry of their wave function. Given that symmetry, there are still many possible different states of two identical electrons.

In the LQG black hole, there are similarly many possible different states of the black hole if one is able to view the state in all its detail. However, to an observer far from the black hole able to probe only some aspects of the state, the different black hole states appear identical. These apparently identical states are thus counted towards the black hole entropy.

Or at least that's the general idea. It's not clear that it really works yet. Some pointers are
http://arxiv.org/abs/0905.4916
http://arxiv.org/abs/1112.0291

Sorry @atyy, but I do not see how you refer to the distinguishability of the horizon states.

However, thanks for the links. Even there it is not really spelled out, how the distinguishability is manifested.

julian
Gold Member
In the LQG calculation the spin network state that describes the bulk geometry (i.e. describes the geometry outside the isolated horizon) punctures the horizon. With each puncture the horizon obtains a quanta of area which depends on the valence of the link puncturing the horizon. The total area of the horizon comes from adding up the areas of each puncture.

However, there will be other spin network states not producing the same set of punctures (different numbers of punctures, different set of valances associated with the punctures) as the original spin network but still give the horizon the same total area.

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Thank you @Julian.

But still, where is the mathematical and physical reason for the distinguishability. What are its consequences? I think this is conceptually very important, since it should decisively coin the state counting, don't you think?

julian
Gold Member
If there are a different number of punctures or the valences (to do with eigenstates of the area operator) are different then it is possible in principle to make measurements that distinguish these states. Like atty said if you were able to view the states in all its detail you would get different results to microscopic measurements.

An interesting point is that you would expect the biggest contribution to the entropy for a macroscopic black hole would be from states that maximize the number of punctures - this corresponds to every puncture having the minimum possible area eigenvalue - then you have the same number of punctures all with the same area eigenvalue. You could then argue that these different states transform into each other by diffeomorphism gauge transformations and shouldn't be counted over. This isn't the case and is a subtle point - it is discussed on pages 310-311 in Rovelli's book.

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julian
Gold Member
I am currently working myself into black hole physics and I am interested in their possible quantum geometric description by means of LQG.

Can anybody please tell me good sources to start with? Since black holes were studied in this framework for a longer time, what is the most recent status?
.

Rovelli's book is a good place to understand the physical ideas behind black hole entropy - I think he was accredited with introducing these ideas - there will be a paper on the archives, probably: arXiv:gr-qc/9603063 "Black Hole Entropy from Loop Quantum Gravity". I also liked his comments in: arXiv:hep-th/0501103 "Black hole entropy: inside or out?" with Ted Jacobson, Donald Marolf, Carlo Rovelli. He talks about the kind of considerations made in the LQG calculation, like sometimes being quantum sometimes classical.

As for the most recent status, the calculation has been generalised to rotating and axis-symmetrically deformed isolated horizons, even progress toward generally deformed isolated horizons (I think maybe). Also progress in giving the isolated horizon a purely quantum mechanical definition. I'd have to look up this stuff..

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thx @julian

"This isn't the case and is a subtle point - it is discussed on pages 310-311 in Rovelli's book."

Ι read the argument today and found it in the corresponding paper

C Rovelli: “Loop Quantum Gravity and Black Hole Physics”, Helvetica Physica Acta, 69 (1996) 582; gr-qc/9608032

However, he wrote there to make the argument more explicit, which wasn't done in the end. Also the big Ashtekar, Krasnov, Baez paper does not highlight the distinguishability or refer to the above paper at the crucial point.

julian
Gold Member
It has been a while, I'll have to try to have another go to understand this stuff better.

A recent review paper was "Quantum isolated horizons and black hole entropy."

I have the impression that this paper played an important role in the formation of the distinguishability point. He claims, if the punctures were supposed to be indistinguishable, one would not arrive at the "proper" BH entropy area relation S~A. I have computed his calculation for both cases but don't arrive at his result :(

Above all, the result is rather a consequence of an assumption. But he does not give an operational justification and mathematical underlying reason for it.

Counting surface states in the loop quantum gravity
Kirill V. Krasnov

We adopt the point of view that (Riemannian) classical and (loop-based) quantum descriptions of geometry are macro- and micro-descriptions in the usual statistical mechanical sense. This gives rise to the notion of geometrical entropy, which is defined as the logarithm of the number of different quantum states which correspond to one and the same classical geometry configuration (macro-state). We apply this idea to gravitational degrees of freedom induced on an arbitrarily chosen in space 2-dimensional surface. Considering an `ensemble' of particularly simple quantum states, we show that the geometrical entropy $S(A)$ corresponding to a macro-state specified by a total area $A$ of the surface is proportional to the area $S(A)=\alpha A$, with $\alpha$ being approximately equal to $1/16\pi l_p^2$. The result holds both for case of open and closed surfaces. We discuss briefly physical motivations for our choice of the ensemble of quantum states

http://arxiv.org/pdf/gr-qc/9603025v3.pdf

Apart from that... more confusing is that there is no sort of Gibbs paradox appearing if one uses distinguishable punctures :surprised

So anybody? I thought this would be an easy question to answer, since the BH entropy explanation from quantum gravitational excitations of the horizon geometry is claimed to be one of the major success stories of LQG.

marcus
Gold Member
Dearly Missed
apparently, there is some sort of changing picture. in the semiclassical regime incl. matter the states seem to have to be indistinguishable.

http://www.perimeterinstitute.ca/vi...ts-and-perspectives-semiclassical-consistency

how can one understand this?

Jason, thanks for calling our attention to that talk! I'm experiencing overload right now with so many interesting talks to watch (sometimes I must even watch a second time). You got me to realize that this overview talk by Perez is exceptionally clear and well presented, so at least the first part is a good pedagogical resource.

Around 13 minutes he starts the specifically quantum treatment.
Around minute 18:30 he points out the distinguishability of the punctures associated with a particular spin network BH state.

He observes that the entropy depends on two effects (a) the spins labeling a fixed number N of punctures and (b) the effect of changing the number N (i.e. the chemical potential).

If you happen to recall, or if it is not too difficult to recover the information, you could tell me roughly around what minute he says what you mention, namely that when matter is included only indistinguishable states are counted. That way I can jump right to that section of the talk and understand your question better.

I may not be able to answer satisfactorily but I would like to understand better what is puzzling you.

EDIT: Ahah! I see where. Around minute 25:35 he includes matter and each puncture is "dressed" by matter degrees of freedom. I think this makes it possible to treat the bare punctures as indistinguishable from each other and still effectively distinguishable in their dressed form. Not sure about this. I'll bet that this is the point in the talk where your question comes up!

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yes, exactly. i find this strange.