Entropy in the classical and quantum polymer black hole models

Etera R. Livine*, Daniel R. Terno

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


We investigate the entropy counting for black hole horizons in loop quantum gravity (LQG). We argue that the space of 3D closed polyhedra is the classical counterpart of the space of SU(2) intertwiners at the quantum level. Then computing the entropy for the boundary horizon amounts to calculating the density of polyhedra or the number of intertwiners at fixed total area. Following the previous work (Bianchi 2011 Class. Quantum Grav. 28 114006) we dub these the classical and quantum polymer models for isolated horizons in LQG. We provide exact micro-canonical calculations for both models and we show that the classical counting of polyhedra accounts for most of the features of the intertwiner counting (leading order entropy and log-correction), thus providing us with a simpler model to further investigate correlations and dynamics. To illustrate this, we also produce an exact formula for the dimension of the intertwiner space as a density of almost-closed polyhedra.

Original languageEnglish
Article number224012
Pages (from-to)1-30
Number of pages30
JournalClassical and Quantum Gravity
Issue number22
Publication statusPublished - 21 Nov 2012


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