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 SIGMA, 2012, Volume 8, 048, 58 pages (Mi sigma725)

Isolated horizons and black hole entropy in Loop Quantum Gravity

Jacobo Diaz-Poloa, Daniele Pranzettib

a Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USA
b Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany

Abstract: 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.

Keywords: black hole entropy, quantum gravity, isolated horizons.

DOI: https://doi.org/10.3842/SIGMA.2012.048

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ArXiv: 1112.0291
MSC: 53Z05; 81S05; 83C57
Received: December 2, 2011; in final form July 18, 2012; Published online August 1, 2012
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Citation: Jacobo Diaz-Polo, Daniele Pranzetti, “Isolated horizons and black hole entropy in Loop Quantum Gravity”, SIGMA, 8 (2012), 048, 58 pp.

Citation in format AMSBIB
\Bibitem{DiaPra12} \by Jacobo Diaz-Polo, Daniele Pranzetti \paper Isolated horizons and black hole entropy in Loop Quantum Gravity \jour SIGMA \yr 2012 \vol 8 \papernumber 048 \totalpages 58 \mathnet{http://mi.mathnet.ru/sigma725} \crossref{https://doi.org/10.3842/SIGMA.2012.048} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2958982} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000306990800001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864835194} 

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This publication is cited in the following articles:
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