A Note on Black Hole Entropy in Loop Quantum Gravity

Abstract

Several recent results have hinted that black hole thermodynamics in loop quantum gravity simplifies if one chooses an imaginary Barbero-Immirzi parameter $\gamma =i$. This suggests a connection with $\mathrm{SL}(2,\mathbb{C})$ or $\mathrm{SL}(2,\mathbb{R})$ conformal field theories at the "boundaries" formed by spin network edges intersecting the horizon. I present a bit of background regarding the relevant conformal field theories, along with some speculations about how they might be used to count black hole states. I show, in particular, that a set of unproven but plausible assumptions can lead to a boundary conformal field theory whose density of states matches the Bekenstein-Hawking entropy.

v2: added references; v3: slight addition to discussion of 3d gravity; v4: more references, typos fixed

References in corpus (3)

• LQG vertex with finite Immirzi parameter
• CFT/Gravity Correspondence on the Isolated Horizon
• BF Theory Explanation of the Entropy for Non-rotating Isolated Horizons

Cited by in corpus (10)

• Constraints on the rotating self-dual black hole with quasi-periodic oscillations
• Constraints on self-dual black hole in loop quantum gravity with S0-2 star in the Galactic Center
• Observational tests of the self-dual spacetime in loop quantum gravity
• Loop quantum cosmology with self-dual variables
• Anisotropic loop quantum cosmology with self-dual variables
• Four-Dimensional Entropy from Three-Dimensional Gravity
• The Conformal Field Theory on the Horizon of BTZ Black Hole
• Entanglement Entropy of Disjoint Spacetime Intervals in Causal Set Theory
• Test of Transitivity in Quantum Field theory using Rindler spacetime
• Selective Thermalization, Chiral Excitations, and a Case of Quantum Hair in the Presence of Event Horizons