The Microcanonical Entropy of Quantum Isolated Horizon, `quantum hair' $N$ and the Barbero-Immirzi parameter fixation

Abstract

{\it If} the total number of punctures($N$) of a quantum isolated horizon is considered to be a macroscopic parameter alongside the Chern-Simons level($k$) or equivalently classical area$(A_{cl})$ a strict analysis of the {\it microcanonical} ensemble reveals that the {\it microcanonical} entropy has the form $S_{MC}=A_{cl}/4{\ell }_p^2+N\sigma (\gamma )$, only for values of the Barbero-Immirzi(BI) parameter$(\gamma )$ greater than a certain number. It is argued that the term $N\sigma (\gamma )$ must be negative definite, which leads to the bound on the BI parameter.

9 pages, 2 figures, drastically modified version, arguments are far more strengthened, an error in the calculation has been rectified which has affected the final result, accepted for publication in Classical and Quantum Gravity

References in corpus (6)

• Black hole entropy and isolated horizons thermodynamics
• The SU(2) Black Hole entropy revisited
• Black Hole Entropy from complex Ashtekar variables
• 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

Cited by in corpus (10)

• Non-extensive Statistical Mechanics and Black Hole Entropy From Quantum Geometry
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• Black Hole Entropy from indistinguishable quantum geometric excitations
• A Discussion on Possible Effects of the Barbero-Immirzi Parameter at the TeV-scale Particle Physics
• Holographic Bound on Area of Compact Binary Merger Remnant
• Thermodynamic partition function from quantum theory for black hole horizons in loop quantum gravity
• Energy spectrum of black holes : a new view
• Stability of Quantum Isolated Horizon : A Local Observer's View
• Can Gravitational Wave Data Shed Light on Dark Matter Particles ?
• Proof of Bekenstein-Mukhanov ansatz in loop quantum gravity