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Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
We review the black hole entropy calculation in the framework of Loop Quantum Gravity based on the quasi-local definition of a black hole encoded in the isolated horizon formalism. We show, by means of the covariant phase space framework, the appearance in the conserved symplectic structure of a bou...
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Інститут математики НАН України
2012
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/148462 |
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irk-123456789-1484622019-02-19T01:24:42Z Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity Diaz-Polo, J. Pranzetti, D. We review the black hole entropy calculation in the framework of Loop Quantum Gravity based on the quasi-local definition of a black hole encoded in the isolated horizon formalism. We show, by means of the covariant phase space framework, the appearance in the conserved symplectic structure of a boundary term corresponding to a Chern-Simons theory on the horizon and present its quantization both in the U(1) gauge fixed version and in the fully SU(2) invariant one. We then describe the boundary degrees of freedom counting techniques developed for an infinite value of the Chern-Simons level case and, less rigorously, for the case of a finite value. This allows us to perform a comparison between the U(1) and SU(2) approaches and provide a state of the art analysis of their common features and different implications for the entropy calculations. In particular, we comment on different points of view regarding the nature of the horizon degrees of freedom and the role played by the Barbero-Immirzi parameter. We conclude by presenting some of the most recent results concerning possible observational tests for theory. 2012 Article Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity / J. Diaz-Polo, D. Pranzetti // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 117 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53Z05; 81S05; 83C57 DOI: http://dx.doi.org/10.3842/SIGMA.2012.048 http://dspace.nbuv.gov.ua/handle/123456789/148462 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
We review the black hole entropy calculation in the framework of Loop Quantum Gravity based on the quasi-local definition of a black hole encoded in the isolated horizon formalism. We show, by means of the covariant phase space framework, the appearance in the conserved symplectic structure of a boundary term corresponding to a Chern-Simons theory on the horizon and present its quantization both in the U(1) gauge fixed version and in the fully SU(2) invariant one. We then describe the boundary degrees of freedom counting techniques developed for an infinite value of the Chern-Simons level case and, less rigorously, for the case of a finite value. This allows us to perform a comparison between the U(1) and SU(2) approaches and provide a state of the art analysis of their common features and different implications for the entropy calculations. In particular, we comment on different points of view regarding the nature of the horizon degrees of freedom and the role played by the Barbero-Immirzi parameter. We conclude by presenting some of the most recent results concerning possible observational tests for theory. |
| format |
Article |
| author |
Diaz-Polo, J. Pranzetti, D. |
| spellingShingle |
Diaz-Polo, J. Pranzetti, D. Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Diaz-Polo, J. Pranzetti, D. |
| author_sort |
Diaz-Polo, J. |
| title |
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity |
| title_short |
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity |
| title_full |
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity |
| title_fullStr |
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity |
| title_full_unstemmed |
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity |
| title_sort |
isolated horizons and black hole entropy in loop quantum gravity |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148462 |
| citation_txt |
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity / J. Diaz-Polo, D. Pranzetti // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 117 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT diazpoloj isolatedhorizonsandblackholeentropyinloopquantumgravity AT pranzettid isolatedhorizonsandblackholeentropyinloopquantumgravity |
| first_indexed |
2023-05-20T17:30:44Z |
| last_indexed |
2023-05-20T17:30:44Z |
| _version_ |
1796153465671516160 |