These people talk as if there might be : ^) http://arxiv.org/abs/1504.05352 Black hole spectroscopy from Loop Quantum Gravity models Aurelien Barrau, Xiangyu Cao, Karim Noui, Alejandro Perez
(Submitted on 21 Apr 2015)
Using Monte Carlo simulations, we compute the integrated emission spectra of black holes in the framework of Loop Quantum Gravity (LQG). The black hole emission rates are governed by the entropy whose value, in recent holographic loop quantum gravity models, was shown to agree at leading order with the Bekenstein-Hawking entropy. Quantum corrections depend on the Barbero-Immirzi parameter γ. Starting with black holes of initial horizon area A∼102 in Planck units, we present the spectra for different values of γ. Each spectrum clearly decomposes in two distinct parts: a continuous background which corresponds to the semi-classical stages of the evaporation and a series of discrete peaks which constitutes a signature of the deep quantum structure of the black hole. We show that γ has an effect on both parts that we analyze in details. Finally, we estimate the number of black holes and the instrumental resolution required to experimentally distinguish between the considered models.
11 pages, 9 figures
But I don't think their idea of holographic LQG models corresponds at level of details to the AdS/CFT picture you suggest in your example.
==excerpt from page 4==
As explained in the introduction, a fundamental understanding of the holographic hypothesis in the models leading to (15) might come from the recent results [24, 25, 33] that indicate a relationship between holography and LQG for complex Ashtekar variables (γ = ±i). ...
You might have a look at their references [24,25,32,33] just in case...
1 does a serious proposal of QG have to respect the holographic principle?
2 if lqg is a serious proposal does it respect the holographic principle?
3 if lqg does respect the holographic proposal, what does it look like?
This is a naive question, I am probably completely missing what is meant by holographic principle, which may be unrelated to the intuitive content I ascribe to these words. But isn't there a kind of holographic principle in any theory of gravity ?
What I mean is, the information an observer has about a system comes from signals this system emits - and such signals must go through any surface enclosing the system : we have no more information about a system than we have about that surface.
If we accept that a system is physically defined by its potential for interacting with (being measured by) other systems, than its state or information content is exhausted by that of the enclosing surface.
I do not understand the idea of giving the holographic principle some fundamental importance.
Ok, if we consider a static homogeneous universe, a large enough homogeneous distribution of matter would have to collapse into a black hole. This could be very large, but its entropy would be that of a black hole, thus, proportional to its surface.
But if we look at the standard cosmological model of an expanding flat homogeneous universe, this effect does not matter. So, whatever the local density of entropy, it is proportional to the volume and not the surface of a region.
If the principle would have some fundamental importance, it could not be so easily circumvented by the expanding universe where we live.