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APS » Journals » Phys. Rev. Lett. » Volume 100 » Issue 21
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Phys. Rev. Lett. 100, 211301 (2008) [4 pages]

Black Hole State Counting in Loop Quantum Gravity: A Number-Theoretical Approach

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Iván Agulló1,*, J. Fernando Barbero G.2,†, Jacobo Díaz-Polo3,‡, Enrique Fernández-Borja1,3,§, and Eduardo J. S. Villaseñor4,2,**
1Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Universidad de Valencia, Burjassot-46100, Valencia, Spain
2Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain
3Departamento de Astronomía y Astrofísica, Universidad de Valencia, Burjassot-46100, Valencia, Spain
4Instituto Gregorio Millán, Grupo de Modelización y Simulación Numérica, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain

Received 12 March 2008; published 27 May 2008

We give an efficient method, combining number-theoretic and combinatorial ideas, to exactly compute black hole entropy in the framework of loop quantum gravity. Along the way we provide a complete characterization of the relevant sector of the spectrum of the area operator, including degeneracies, and explicitly determine the number of solutions to the projection constraint. We use a computer implementation of the proposed algorithm to confirm and extend previous results on the detailed structure of the black hole degeneracy spectrum.

© 2008 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.100.211301
DOI:
10.1103/PhysRevLett.100.211301
PACS:
04.70.Dy, 04.60.Pp

*Ivan.Agullo@uv.es

†Corresponding author.

fbarbero@iem.cfmac.csic.es

‡Jacobo.Diaz@uv.es

§Enrique.Fernandez@uv.es

**ejsanche@math.uc3m.es

 
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