Abstract
In 1996, Rovelli suggested a connection between black hole entropy and the area spectrum. Using this formalism and a theorem we prove in this paper, we briefly show the procedure to calculate the quantum corrections to the Bekenstein–Hawking entropy. One can do this by two steps. First, one can calculate the “naive” black hole degeneracy without the projection constraint (in case of the \(U(1)\) symmetry reduced framework) or the \(SU(2)\) invariant subspace constraint (in case of the fully \(SU(2)\) framework). Second, then one can impose the projection constraint or the \(SU(2)\) invariant subspace constraint, obtaining logarithmic corrections to the Bekenstein–Hawking entropy. In this paper, we focus on the first step and show that we obtain infinite relations between the area spectrum and the naive black hole degeneracy. Promoting the naive black hole degeneracy into its approximation, we obtain the full solution to the infinite relations.
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Acknowledgments
We thank Jong-Hyun Baek for the helpful and crucial discussions. This work was supported by the National Research Foundation of Korea (NRF) grants 2012R1A1B3001085 and 2012R1A2A2A02046739.
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Yoon, Y. Approximation of the naive black hole degeneracy. Gen Relativ Gravit 45, 373–386 (2013). https://doi.org/10.1007/s10714-012-1475-8
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DOI: https://doi.org/10.1007/s10714-012-1475-8