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marcus

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**Bianchi's entropy result--what to ask, what to learn from it**

I think most if not all here are familiar with the idea that entropy, by definition, is not an absolute but depends on the observer. (Padmanabhan loves to make that point. :-D) There may also be an explicit scale-dependence. And in the Loop context one expects the Immirzi parameter to run with scale.

Likewise black hole horizon

**temperature**is highly dependent on how far away the observer is hovering. So there is this interesting and suggestive nexus of ideas that we need to pick apart and learn something from. Bianchi has just made a significant contribution to this.

http://arxiv.org/abs/1204.5122

**Entropy of Non-Extremal Black Holes from Loop Gravity**

Eugenio Bianchi

(Submitted on 23 Apr 2012)

We compute the entropy of non-extremal black holes using the quantum dynamics of Loop Gravity. The horizon entropy is finite, scales linearly with the area A, and reproduces the Bekenstein-Hawking expression S = A/4 with the one-fourth coefficient for all values of the Immirzi parameter. The near-horizon geometry of a non-extremal black hole - as seen by a stationary observer - is described by a Rindler horizon. We introduce the notion of a quantum Rindler horizon in the framework of Loop Gravity. The system is described by a quantum surface and the dynamics is generated by the boost Hamiltonion of Lorentzian Spinfoams. We show that the expectation value of the boost Hamiltonian reproduces the local horizon energy of Frodden, Ghosh and Perez. We study the coupling of the geometry of the quantum horizon to a two-level system and show that it thermalizes to the local Unruh temperature. The derived values of the energy and the temperature allow one to compute the thermodynamic entropy of the quantum horizon. The relation with the Spinfoam partition function is discussed.

6 pages, 1 figure