Quantum Geometry and Black Hole Entropy

Quantum Geometry and Black Hole Entropy

1 Oct 1997 | A. Ashtekar1, J. Baez2, A. Corichi1,3, K. Krasnov1
The paper introduces a non-perturbative quantum gravity framework to study black hole entropy, focusing on non-rotating, uncharged black holes. The authors construct a sector of the classical phase space corresponding to these black holes and quantize it using Chern-Simons theory. They find that the entropy of a large non-rotating black hole is proportional to its horizon area, with the proportionality constant depending on the Immirzi parameter. This parameter, which fixes the spectrum of the area operator in loop quantum gravity, allows for the Bekenstein-Hawking formula \( S = A/4\ell_P^2 \) to be satisfied. The same choice of the Immirzi parameter also holds for black holes with electric or dilatonic charges. The paper discusses the classical and quantum aspects of the phase space, the quantization process, and the resulting Hilbert spaces for volume and surface states. It concludes by highlighting the consistency of the results across different black hole models and the potential implications for black hole evaporation.The paper introduces a non-perturbative quantum gravity framework to study black hole entropy, focusing on non-rotating, uncharged black holes. The authors construct a sector of the classical phase space corresponding to these black holes and quantize it using Chern-Simons theory. They find that the entropy of a large non-rotating black hole is proportional to its horizon area, with the proportionality constant depending on the Immirzi parameter. This parameter, which fixes the spectrum of the area operator in loop quantum gravity, allows for the Bekenstein-Hawking formula \( S = A/4\ell_P^2 \) to be satisfied. The same choice of the Immirzi parameter also holds for black holes with electric or dilatonic charges. The paper discusses the classical and quantum aspects of the phase space, the quantization process, and the resulting Hilbert spaces for volume and surface states. It concludes by highlighting the consistency of the results across different black hole models and the potential implications for black hole evaporation.
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