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Ashtekar, A.; Baez, J.; Corichi, A.; Krasnov, K.

Quantum geometry and black hole entropy. (English) Zbl 0949.83024

Phys. Rev. Lett. 80, No. 5, 904-907 (1998).
Summary: A ‘black hole sector’ of nonperturbative canonical quantum gravity is introduced. The quantum black hole degrees of freedom are shown to be described by a Chern-Simons field theory on the horizon. It is shown that the entropy of a large nonrotating black hole is proportional to its horizon area. The constant of proportionality depends upon the Immirzi parameter, which fixes the spectrum of the area operator in loop quantum gravity; an appropriate choice of this parameter gives the Bekenstein-Hawking formula \(S=A/4l^2_{\text{P}}\). With the same choice of the Immirzi parameter, this result also holds for black holes carrying electric or dilatonic charges, which are not necessarily near extremal.

Cited in 162 Documents

MSC:

83C45 Quantization of the gravitational field
83C57 Black holes

Keywords:

canonical quantum gravity; Chern-Simons field theory; Bekenstein-Hawking formula \(S= A/4l_P^2\); Immirzi parameter
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\textit{A. Ashtekar} et al., Phys. Rev. Lett. 80, No. 5, 904--907 (1998; Zbl 0949.83024)
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