Quantum Hairs and Entropy of Quantum Isolated Horizon from Chern-Simons Theory

Abstract

We articulate the fact that the loop quantum gravity description of the quantum macrostates of black hole horizons, modeled as Quantum Isolated Horizons (QIHs), is completely characterized in terms of two independent integer-valued `quantum hairs', viz,. the coupling constant $(k)$ of the quantum $SU(2)$ Chern-Simons theory describing QIH dynamics, and the number of punctures $(N)$ produced by the bulk spin network edges piercing the isolated horizon (which act as pointlike sources for the Chern- Simons fields). We demonstrate that the microcanonical entropy of macroscopic (both parameters assuming very large values) QIHs can be obtained directly from the microstates of this Chern-Simons theory, using standard statistical mechanical methods, without having to additionally postulate the horizon as an ideal gas of punctures, or incorporate any additional classical or semi-classical input from general relativity vis-a-vis the functional dependence of the IH mass on its area, or indeed, without having to restrict to any special class of spins. Requiring the validity of the Bekenstein-Hawking area law relates these two parameters (as an equilibrium `equation of state') and consequently allows the Barbero-Immirzi parameter to take any real and positive value depending on the value of $k/N$. The logarithmic correction to the area law obtained a decade ago by R. Kaul and one of us (P.M.), ensues straightforwardly, with precisely the coefficient -3/2, making it a signature of the loop quantum gravity approach to black hole entropy.

11 pages, version accepted for publication in Classical and Quantum Gravity

References in corpus (6)

• Topological Interpretation of Barbero-Immirzi Parameter
• Counting black hole microscopic states in loop quantum gravity
• Fine-grained state counting for black holes in loop quantum gravity
• Radiation from quantum weakly dynamical horizons in LQG
• Generalized Hawking-Page Phase Transition
• Dynamical evaporation of quantum horizons

Cited by in corpus (11)

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• A Discussion on Possible Effects of the Barbero-Immirzi Parameter at the TeV-scale Particle Physics
• Quantum black holes, partition of integers and self-similarity
• Holographic Bound on Area of Compact Binary Merger Remnant
• Conformal blocks on a 2-sphere with indistinguishable punctures and implications on black hole entropy
• Thermodynamic partition function from quantum theory for black hole horizons in loop quantum gravity
• Energy spectrum of black holes : a new view
• Can Gravitational Wave Data Shed Light on Dark Matter Particles ?