Agradecimientos:
We would like to thank John Baez for pointing out the relation with the quasinormal modes. We also thank Alejandro Corichi for drawing our attention to several references. This work was partially supported by the Spanish MICINN research grant FIS2008-03221, the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042), the Polish Ministerstwo Nauki i Szkolnictwa Wyzszego grants 1 P03B 075 29, 182/N-QGG/2008/0, and by 2007-2010 research project N202 n081 32/1844, the National Science Foundation (NSF) grant PHY-0456913 and by the Foundation for Polish Science grant Master. F. Barbero acknowledges the financial support provided by the European Science Foundation Short Visit Grant "A new approach to the study of black hole entropy in loop quantum gravity" within the framework of the activity titled ‘"Quantum Geometry and Quantum Gravity".
We show that, for space-times with inner boundaries, there exists a natural area operator different from the standard one used in loop quantum gravity. This new flux-area operator has equidistant eigenvalues. We discuss the consequences of substituting the staWe show that, for space-times with inner boundaries, there exists a natural area operator different from the standard one used in loop quantum gravity. This new flux-area operator has equidistant eigenvalues. We discuss the consequences of substituting the standard area operator in the Ashtekar-Baez-Corichi-Krasnov definition of black hole entropy by the new one. Our choice simplifies the definition of the entropy and allows us to consider only those areas that coincide with the one defined by the value of the level of the Chern-Simons theory describing the horizon degrees of freedom. We give a prescription to count the number of relevant horizon states by using spin components and obtain exact expressions for the black hole entropy. Finally we derive its asymptotic behavior, discuss several issues related to the compatibility of our results with the Bekenstein-Hawking area law and the relation with Schwarzschild quasi-normal modes.[+][-]
