Entropy of Quantum Black Holes
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 develop...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2012 |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148368 |
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| Cite this: | Entropy of Quantum Black Holes / R.K. Kaul // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 55 назв. — англ. |
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Kaul, R.K. 2019-02-18T11:04:09Z 2019-02-18T11:04:09Z 2012 Entropy of Quantum Black Holes / R.K. Kaul // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 55 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81T13; 81T45; 83C57; 83C45; 83C47 DOI: http://dx.doi.org/10.3842/SIGMA.2012.005 https://nasplib.isofts.kiev.ua/handle/123456789/148368 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. This paper is a contribution to the Special Issue “Loop Quantum Gravity and Cosmology”. The full collection is available at http://www.emis.de/journals/SIGMA/LQGC.html. The author gratefully acknowledges collaborations with T.R. Govindarajan, P. Majumdar, S. Kalyana Rama and V. Suneeta which have lead to many of the results surveyed here. Thanks are also due to Ghanashyam Date for his useful comments. The support of the Department of Science and Technology, Government of India, through a J.C. Bose National Fellowship is gratefully acknowledged. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Entropy of Quantum Black Holes Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Entropy of Quantum Black Holes |
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Entropy of Quantum Black Holes Kaul, R.K. |
| title_short |
Entropy of Quantum Black Holes |
| title_full |
Entropy of Quantum Black Holes |
| title_fullStr |
Entropy of Quantum Black Holes |
| title_full_unstemmed |
Entropy of Quantum Black Holes |
| title_sort |
entropy of quantum black holes |
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Kaul, R.K. |
| author_facet |
Kaul, R.K. |
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2012 |
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English |
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Symmetry, Integrability and Geometry: Methods and Applications |
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Інститут математики НАН України |
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Article |
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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.
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| issn |
1815-0659 |
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https://nasplib.isofts.kiev.ua/handle/123456789/148368 |
| citation_txt |
Entropy of Quantum Black Holes / R.K. Kaul // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 55 назв. — англ. |
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