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SIGMA, 2012, Volume 8, 005, 30 pages (Mi sigma682)  

This article is cited in 20 scientific papers (total in 20 papers)

Entropy of quantum black holes

Romesh K. Kaul

The Institute of Mathematical Sciences, CIT Campus, Chennai-600 113, India

Abstract: In the Loop Quantum Gravity, black holes (or even more general Isolated Horizons) are described by a $SU(2)$ Chern–Simons theory. There is an equivalent formulation of the horizon degrees of freedom in terms of a $U(1)$ gauge theory which is just a gauged fixed version of the $SU(2)$ theory. These developments will be surveyed here. Quantum theory based on either formulation can be used to count the horizon micro-states associated with quantum geometry fluctuations and from this the micro-canonical entropy can be obtained. We shall review the computation in $SU(2)$ formulation. Leading term in the entropy is proportional to horizon area with a coefficient depending on the Barbero–Immirzi parameter which is fixed by matching this result with the Bekenstein–Hawking formula. Remarkably there are corrections beyond the area term, the leading one is logarithm of the horizon area with a definite coefficient $-3/2$, a result which is more than a decade old now. How the same results are obtained in the equivalent $U(1)$ framework will also be indicated. Over years, this entropy formula has also been arrived at from a variety of other perspectives. In particular, entropy of BTZ black holes in three dimensional gravity exhibits the same logarithmic correction. Even in the String Theory, many black hole models are known to possess such properties. This suggests a possible universal nature of this logarithmic correction.

Keywords: black holes, micro-canonical entropy, topological field theories; $SU(2)$ Chern–Simons theory, Isolated Horizons, Bekenstein–Hawking formula, logarithmic correction, Barbero–Immirzi parameter, conformal field theories, Cardy formula, BTZ black hole, canonical entropy.

DOI: https://doi.org/10.3842/SIGMA.2012.005

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Full text: http://emis.mi.ras.ru/.../005
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Bibliographic databases:

ArXiv: 1201.6102
MSC: 81T13, 81T45, 83C57, 83C45, 83C47
Received: September 14, 2011; in final form February 3, 2012; Published online February 8, 2012
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Citation: Romesh K. Kaul, “Entropy of quantum black holes”, SIGMA, 8 (2012), 005, 30 pp.

Citation in format AMSBIB
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\by Romesh K. Kaul
\paper Entropy of quantum black holes
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\papernumber 005
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    This publication is cited in the following articles:
    1. Livine E.R., Terno D.R., “Entropy in the Classical and Quantum Polymer Black Hole Models”, Class. Quantum Gravity, 29:22 (2012), 224012  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Lochan K. Vaz C., “Statistical Analysis of Entropy Correction From Topological Defects in Loop Black Holes”, Phys. Rev. D, 86:4 (2012), 044035  crossref  mathscinet  adsnasa  isi  elib  scopus
    3. Lochan K., Vaz C., “Canonical Partition Function of Loop Black Holes”, Phys. Rev. D, 85:10 (2012), 104041  crossref  adsnasa  isi  elib  scopus
    4. Pithis A.G.A., “Gibbs Paradox, Black Hole Entropy, and the Thermodynamics of Isolated Horizons”, Phys. Rev. D, 87:8 (2013), 084061  crossref  adsnasa  isi  elib  scopus
    5. Livine E.R., “Deformations of Polyhedra and Polygons by the Unitary Group”, J. Math. Phys., 54:12 (2013), 123504  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Sen A., “Logarithmic Corrections to Schwarzschild and Other Non-Extremal Black Hole Entropy in Different Dimensions”, J. High Energy Phys., 2013, no. 4, 156  crossref  mathscinet  isi  scopus
    7. Livine E.R., “Deformation Operators of Spin Networks and Coarse-Graining”, Class. Quantum Gravity, 31:7 (2014), 075004  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Majhi A., “The Microcanonical Entropy of Quantum Isolated Horizon, ‘Quantum Hair’ N and the Barbero-Immirzi Parameter Fixation”, Class. Quantum Gravity, 31:9 (2014), 095002  crossref  zmath  adsnasa  isi  scopus
    9. Wang J. Ma Y. Zhao X.-A., “Bf Theory Explanation of the Entropy for Nonrotating Isolated Horizons”, Phys. Rev. D, 89:8 (2014), 084065  crossref  adsnasa  isi  scopus
    10. Majhi A., Majumdar P., “‘Quantum Hairs’ and Entropy of the Quantum Isolated Horizon From Chern-Simons Theory”, Class. Quantum Gravity, 31:19 (2014), 195003  crossref  mathscinet  zmath  adsnasa  isi  scopus
    11. Sengupta S., “Dark Energy From the Gravity Vacuum”, Class. Quantum Gravity, 32:19 (2015), 195005  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. Pradhan P., “Horizon Straddling Iscos in Spherically Symmetric String Black Holes”, Int. J. Mod. Phys. D, 24:11 (2015), 1550086  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    13. A. G. A. Pithis, H.-C. Ruiz Euler, “Anyonic statistics and large horizon diffeomorphisms for loop quantum gravity black holes”, PHYSICAL REVIEW D, 91:6 (2015), 064053  crossref  mathscinet  elib  scopus
    14. Majhi A., “Conformal blocks on a 2-sphere with indistinguishable punctures and implications on black hole entropy”, Phys. Lett. B, 762 (2016), 243–246  crossref  mathscinet  zmath  isi  scopus
    15. Majhi A., “Black Hole Entropy from Indistinguishable Quantum Geometric Excitations”, Adv. High. Energy Phys., 2016, 2903867  crossref  mathscinet  zmath  isi  scopus
    16. A. Majhi, “Energy spectrum of black holes: A new view”, Mod. Phys. Lett. A, 32:2 (2017), 1750002  crossref  mathscinet  zmath  isi  scopus
    17. P. Bargueno, S. Bravo Medina, M. Nowakowski, D. Batic, “Quantum-mechanical corrections to the Schwarzschild black-hole metric”, EPL, 117:6 (2017), 60006  crossref  isi  scopus
    18. E. R. Livine, “Intertwiner entanglement on spin networks”, Phys. Rev. D, 97:2 (2018), 026009  crossref  mathscinet  isi  scopus
    19. Dittrich B., Goeller Ch., Livine E.R., Riello A., “Quasi-Local Holographic Dualities in Non-Perturbative 3D Quantum Gravity i - Convergence of Multiple Approaches and Examples of Ponzano-Regge Statistical Duals”, Nucl. Phys. B, 938 (2019), 807–877  crossref  mathscinet  zmath  isi  scopus
    20. Chakraborty S., Lochan K., “Decoding Infrared Imprints of Quantum Origins of Black Holes”, Phys. Lett. B, 789 (2019), 276–286  crossref  mathscinet  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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