Recently, I read a beautiful paper in which it is proven that ANY surface in LQG contains degeneracy, no matter it being a boundary horizon or whatever else. (http://uk.arxiv.org/abs/gr-qc/0603121) This degeneracy is such that the surface degeneracy is A/4. This is a critial discovery in LQG and can follow up Padmanabhan's idea of associating the lack of information in (http://uk.arxiv.org/abs/gr-qc/0405072) into quantum gravity.(adsbygoogle = window.adsbygoogle || []).push({});

So far, Astekar-Baez-krasnov-Corichi in (http://uk.arxiv.org/abs/gr-qc/9710007) were trying to convince folk that if one treats a horizon as a boundary of space at which the space ends, some independent degrees of freedom appears on the boundary.

What physical condition does force one to think about the horizon as the 2-surface at which the space is terminated? This kind of horizon even if classically work, in quantum space is far away from reality. To me, this picture is not convincing. Ansari raises a physical problem against the ABKC model. He says "In classical general relativity, the spacetime metric extends to the interior of the black hole. Thus there is a need for a quantum description of a black hole spacetime that also includes the interior. To do this, we need to identify the horizon within a state that represents the whole quantum geometry."

"Here, I propose that the horizon can be defined in terms of a partition that splits the manifold into two disjoint sections. In loop quantum gravity an eigenstate of quantum geometry is a spin network state. Therefore,

the horizon will be identified within the part of the spin network that lies in a boundary that separates the two regions."

"One immediate consequence of this definition is that the horizon geometry emerges from the contribution of all states of the near horizon region. By introducing the notion of degeneracy of spin network states, it turns out that the horizon states are degenerate."

If he is right, he has found a critial point in LQG which is extremely useful for the purpose of understanding the meaning of "geometrical Quantization".

What comes right is based on how physically different are ABKC's picture and Ansari's new proposal.

Danny

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"I like this universe! Don't you?"

http://uk.arxiv.org/abs/hep-th/0409182

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# Ansari's degeneracy in LQG

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