Immirzi 0.274 (Meissner+Ghosh+Mitra+Corichi et al)

[marcus]

In http://arxiv.org/abs/gr-qc/0407052 Meissner gave two possible values for the Immirzi, a number important in QG. On page 3 one sees

0.23753295796592... and also 0.273985635...

AFAIK this paper is the first place the two numbers appeared. It was a correction of some earlier estimated bounds involving log 2 and log 3 and pi.

Meissner thought that the first (0.237...) was right, but he said with a different assumption you get the other (about 0.274)

Then, in a series of papers Ghosh and Mitra said that the second one, 0.274, was the right one. They were counting black hole states by brute force. Anyway that is how it looks to me---see for yourself:

http://arxiv.org/abs/gr-qc/0401070
http://arxiv.org/abs/gr-qc/0411035
http://arxiv.org/abs/gr-qc/0603029

You must judge for yourself. I am persuaded that the earlier researchers (Ashtekar, Baez, Krasnov...) were almost right with the log 2 etc. and that Meissner was closer still. But I think Ghosh and Mitra hit it. I think it is 0.274 and it will stay that way now.

At one time people were citing papers about Black Hole VIBRATIONS in connection with this but I don't see any references to this any more in the recent papers. the "quasi-normal mode" (QNM) calculations were classical and apparently are not now considered relevant.

Of particular interest in the new work is a LOG CORRECTION TERM. Ghosh and Mitra are concerned with determining the coefficient of that term.

At this point there comes a new paper by Corichi et al. They used numerical methods (computer) to count the states in small black holes and graph the results, and fit curves.

http://arxiv.org/abs/gr-qc/0605014

The entropy is NOT simply equal to 1/4 of the area. The ratio depends on the size of the hole and there are correction terms.
So Corichi et al explore the regime of small holes and get plots. they find the number that fits is 0.274.
So that is good news for Ghosh and Mitra.

 

[marcus]

new today
http://arxiv.org/abs/hep-th/0605125
Counting of isolated horizon states
A. Ghosh, P. Mitra
4 pages
"The entropy of an isolated horizon has been obtained by counting states in loop quantum gravity. We revisit the calculation of the horizon states using statistical methods and find the possibility of additional states, leading to an increase in the entropy. Apart from this, an isolated horizon temperature is introduced in this framework."

this paper of Ghosh and Mitra cites this recent one of Corichi et al
http://arxiv.org/abs/gr-qc/0605014
Entropy counting for microscopic black holes in LQG
Alejandro Corichi, Jacobo Diaz-Polo, Enrique Fernandez-Borja
4 pages, 6 figures

"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 A₀ are computed and the statistical entropy, as a function of the area, is obtained for A₀ up to 550 L²_P 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 unexpected functional form for the entropy is found for small, Planck size, black holes that calls for a physical interpretation."

The paper of Ghosh Mitra that appeared today also cites one of theirs that was published in Physical Review Letters B, in 2005. It has the same value of the Immirzi parameter, namely about 0.274.

http://arxiv.org/abs/gr-qc/0411035
An improved estimate of black hole entropy in the quantum geometry approach
A. Ghosh, P. Mitra
5 pages, LaTeX
Journal-ref: 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."

 

[Entropia]

They said it was 0.274 all along.

Thank you for the detailed explanation and summary of the research on the Immirzi parameter. It is interesting to see how the value of this parameter has evolved over time and how different researchers have approached its determination. It is also fascinating to see the use of various methods such as brute force counting and numerical simulations to determine the value of this parameter. The fact that there is still ongoing research and debate about its exact value shows the complexity and importance of this parameter in quantum gravity. I look forward to seeing further developments in this field and how it may contribute to our understanding of black holes and the nature of spacetime.