# A minor Immirzi revolution (Corichi, Ghosh, DeBenedictis)

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## Main Question or Discussion Point

A minor Immirzi scuffle (Corichi, Ghosh, DeBenedictis)

Andrew DeBenedictis and two friends just came out with a paper that will stir up Immirzi controversy.
http://arxiv.org/abs/gr-qc/0702036

Already there have been series of papers on the one hand by Corichi et al and on the other by Ghosh and Mitra both of which say that the Immirzi parameter should be 0.274...

that is, it should be the solution of a certain transcendental equation found by Ghosh. (possible pun---by guess and by Ghosh)

This came from studying black holes with SPHERICAL event horizon.

The DeBenedictis paper investigates something wholely (holely) different, a TOROIDAL black hole event horizon. And it counts states and computes entropy and compares with area, just like you are supposed to, and it GETS THE SAME IMMIRZI of 0.274... satisfying the same transcendental equation.

this is disturbing because it raises supicions that the figure of 0.274 might actually be right!

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http://arxiv.org/abs/gr-qc/0702036
Phase-space and Black Hole Entropy of Toroidal Horizons in Loop Quantum Gravity
S. Kloster, J. Brannlund, A. DeBenedictis
14 pages, 6 figures

"In the context of loop quantum gravity, we construct the phase-space of the isolated horizon with toroidal topology. Within the loop quantum gravity framework, this horizon is described by a torus with N punctures and the dimension of the corresponding phase-space is calculated including the toroidal cycles as degrees of freedom. From this, the black hole entropy can be calculated by counting the microstates which correspond to a black hole of fixed area. We find that the leading term agrees with the A/4 law and that the sub-leading contribution is modified by the toroidal cycles."

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To save trouble looking them up, I'll get links for Corich and Ghosh papers

http://arxiv.org/abs/hep-th/0605125
Counting black hole microscopic states in loop quantum gravity
Amit Ghosh, Parthasarathi Mitra
5 pages, to appear in PRD
Phys.Rev. D74 (2006) 064026

"Counting of microscopic states of black holes is performed within the framework of loop quantum gravity. This is the first calculation of the pure horizon states using statistical methods, which reveals the possibility of additional states missed in the earlier calculations, leading to an increase of entropy. Also for the first time a microcanonical temperature is introduced within the framework."

Physical Review Series D is a good place to be published. I had not registered yet than Ghosh has gotten so far with this 0.274 value of the Immirzi.

http://arxiv.org/gr-qc/0411035 [Broken]
An improved estimate of black hole entropy in the quantum geometry approach
Amit Ghosh, Parthasarathi Mitra
5 pages
Phys.Lett. B616 (2005) 114-117

"A proper counting of states for black holes in the quantum geometry approach shows that the dominant configuration for spins are distributions that include spins exceeding one-half at the punctures. This raises the value of the Immirzi parameter and the black hole entropy. However, the coefficient of the logarithmic correction remains -1/2 as before."

This is certain to be on the agenda at the Morelia conference this summer that Francesca gave us news about----the Mexico-style LOOPS '07.

http://arxiv.org/abs/gr-qc/0605014
Quantum geometry and microscopic black hole entropy
Alejandro Corichi, Jacobo Diaz-Polo, Enrique Fernandez-Borja
10 pages, 7 new figures.
Class.Quant.Grav. 24 (2007) 243-251

"Quantum black holes within the loop quantum gravity (LQG) framework are considered. The number of microscopic states that are consistent with a black hole of a given horizon area $A_0$ are counted and the statistical entropy, as a function of the area, is obtained for $A_0$ up to $550 l^2_{\rm Pl}$. The results are consistent with an asymptotic linear relation and a logarithmic correction with a coefficient equal to -1/2. The Barbero-Immirzi parameter that yields the asymptotic linear relation compatible with the Bekenstein-Hawking entropy is shown to coincide with a value close to $\gamma=0.274$, which has been previously obtained analytically. However, a new and oscillatory functional form for the entropy is found for small, Planck size, black holes that calls for a physical interpretation."

IMHO all this work is fairly impressive. Look for instance at Corichi's graphs. There is a lot of numerical work that comes out close to the analytical result of 0.274. It makes it hard to avoid the conclusion. On the analytical side, Ghosh work seems very solid. Now on top of that comes this TOROID result unexpectedly from a different direction. DeBenedictis and his co-authors are new to non-string QG and they are up in Canada somewhere. This goes against the Polish work of a few years back. Could it be right?

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It's a bit of a stretch to call it a revolution. A revolution to me is a change in direction; this seems more of an extension of previous work.

I think the real revolution will be when someone properly justifies why the quantity they call the black hole entropy has anything to do with the real black hole entropy - the one that Hawking calculated. This justification should include a proof that this quantity called entropy increases with time. Once this is done we will have a good basis to choose which of the half dozen or so values of the Immirzi parameter is the right one.

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It's a bit of a stretch to call it a revolution. A revolution to me is a change in direction; this seems more of an extension of previous work.

I think the real revolution will be when someone properly justifies why the quantity they call the black hole entropy has anything to do with the real black hole entropy - the one that Hawking calculated. This justification should include a proof that this quantity called entropy increases with time. Once this is done we will have a good basis to choose which of the half dozen or so values of the Immirzi parameter is the right one.
You know Donnelly, the very minute I posted that I had the idea that revolution was the wrong word and I should have said it was a SCUFFLE over the Immirzi.
But unfortunately the software doesnt allow changes in the Forum menu!

But I did the best i could: I changed it to scuffle in the post itself. Hope this is some consolation :-)

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Today DeBenedictis will present a talk here in Zagreb, Croatia. I will be there, of course. Here is the summary of his talk:

Black Hole Entropy from Loop Quantum Gravity

Loop quantum gravity is becoming a promising theory of quantum
gravity that seems to reconcile concepts of quantum mechanics with those
of general relativity. In this talk I will briefly review the loop
quantum gravity program and discuss how to construct the phase-space
relevant for isolated black hole horizons. Special emphasis will be paid
to horizons with exotic topology (toroidal). By counting the number of
quantum states which correspond to a surface with classical area $A$,
the entropy of the black hole is calculated and the $A/4$ law is recovered.

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Today DeBenedictis will present a talk here in Zagreb, Croatia. I will be there, of course...

Black Hole Entropy from Loop Quantum Gravity
...
I am glad to hear about it. the talk has probably already occurred since it is almost 10 AM pacific.

Steve Carlip just posted two papers on arxiv about BH entropy.
He points out that several different QG approaches agree about it and looks for a way to understand this. He asks why should very different approaches, with very different ways of counting states, converge on the same or similar answers. Carlip's viewpoint is helpful because he doesn't seem to favor any particular approach---he looks at all on a more or less equal footing.

I was interested to read about Benedictis et al paper because it arrived at the same value of the Immirzi parameter that some other recent work did----that 0.274 number.