In connection with the long saga of the (claimed) microscopic calculations of the Hawking-Bekenstein entropy in (3+1) Loop Quantum Gravity (LQG) and related approaches I have the following question: Ignoring the question of the overall coefficient, what is the most clearly articulated argument that the entropy satisfies an area law in the first place?

For example, in A. Ashtekar, J. Baez, A. Corichi, K. Krasnov, http://arxiv.org/abs/gr-qc/9710007, I read

It is intuitively clear that not all the degrees of freedom described by fields $^\gamma A$, $^\gamma\Sigma$ are relevant to the problem of black hole entropy. In particular, there are ‘volume’ degrees of freedom in the theory corresponding to gravitational waves far away from $\Delta$ which should not be taken into account as genuine black hole degrees of freedom. The ‘surface’ degrees of freedom describing the geometry of the horizon S have a different status. It has often been argued (see, e.g., [3] and references therein) that it is the degrees of freedom ‘living on the horizon’ that should account for the entropy. We adopt this viewpoint in our approach.

This does not really say that the area law can be derived. It only says that the entropy 'should' be dominated by surface degrees of freedom. Are there any papers in the literature in which an area law is derived?

  • $\begingroup$ Nice question +1. If you dont get a nice answer here or too many IQ statements, you can probably ask this alternatively here ;-) $\endgroup$
    – Dilaton
    Commented May 14, 2012 at 23:27
  • $\begingroup$ What are the usual IQ statements??? I don't understand what that means. $\endgroup$
    – kηives
    Commented May 15, 2012 at 0:10
  • $\begingroup$ @kηives Loop Quantum Gravity is a controversial subject for many theoretical physicists, for some of them to the point of comments referring disparagingly to the intelligence of the people working in that field; that is the "IQ statements" $\endgroup$
    – anna v
    Commented May 15, 2012 at 6:55
  • $\begingroup$ @kηives Anna is right but dont worry, it is obviously not that bad here :-) $\endgroup$
    – Dilaton
    Commented May 15, 2012 at 7:36

1 Answer 1


In Rovelli's book "Quantum Gravity", not only does he make that claim, he derives the area law straight from LQG. He also gives references for more detailed derivations. They are


"Modern Canonical Quantum Gravity" T. Thiemann- gr-qc/0110034

along with the reference you cited.

Also in Rovelli's book, in his Bibliographical notes for chapter 8 he gives a couple more different references for LQG and black holes. They are

K. Krasnov Phys. Rev. D55 (1997) 3505

K. Krasnov Gen. Rel. Grav. 30 (1998) 53-68 and gr-qc/9605047

K. Krasnov Gen. Rel. Grav. 30 (1998) 53

C. Rovelli Phys. Rev. Lett. 14 (1996) 3288

  • $\begingroup$ Thanks. I haven't looked at all of these, obviously. But consider the first paper. From the abstract: ``For macroscopic black holes, the logarithm of the number of these horizon microstates is proportional to the area, irrespective of the values of (non-gravitational) charges''. Doesn't that also say that if the entropy comes from the horizon states, then it is proportional to the area? $\endgroup$
    – Thomas
    Commented May 15, 2012 at 2:10
  • $\begingroup$ This is not really an answer to a question which is skeptical of claims--- you can't cite people making the claims, you have to explain why their calculation is justified. $\endgroup$
    – Ron Maimon
    Commented May 15, 2012 at 3:02
  • $\begingroup$ I just thought that the main question was "Are there any papers in the literature that do make that claim?" That's all I meant to answer. The OP seemed thankful... I'm sorry you're not satisfied... $\endgroup$
    – kηives
    Commented May 15, 2012 at 3:11
  • 1
    $\begingroup$ @kηives: The OP is skeptical of the claim, he is asking "are they doing it right", so he is not satisfied, but it's not a bad answer, it good literature pointers. I was making the comment to help others who might want to think about doing another answer. $\endgroup$
    – Ron Maimon
    Commented May 15, 2012 at 5:01

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