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Article Dans Une Revue Journal of High Energy Physics Année : 2013

Statistical Entropy of a BTZ Black Hole from Loop Quantum Gravity

Résumé

We compute the statistical entropy of a BTZ black hole in the context of three-dimensional Euclidean loop quantum gravity with a cosmological constant $\Lambda$. As in the four-dimensional case, a quantum state of the black hole is characterized by a spin network state. Now however, the underlying colored graph $\Gamma$ lives in a two-dimensional spacelike surface $\Sigma$, and some of its links cross the black hole horizon, which is viewed as a circular boundary of $\Sigma$. Each link $\ell$ crossing the horizon is colored by a spin $j_\ell$ (at the kinematical level), and the length $L$ of the horizon is given by the sum $L=\sum_\ell L_\ell$ of the fundamental length contributions $L_\ell$ carried by the spins $j_\ell$ of the links $\ell$. We propose an estimation for the number $N^\text{BTZ}_\Gamma(L,\Lambda)$ of the Euclidean BTZ black hole microstates (defined on a fixed graph $\Gamma$) based on an analytic continuation from the case $\Lambda>0$ to the case $\Lambda<0$. In our model, we show that $N^\text{BTZ}_\Gamma(L,\Lambda)$ reproduces the Bekenstein-Hawking entropy in the classical limit. This asymptotic behavior is independent of the choice of the graph $\Gamma$ provided that the condition $L=\sum_\ell L_\ell$ is satisfied, as it should be in three-dimensional quantum gravity.

Dates et versions

hal-00957632 , version 1 (10-03-2014)

Identifiants

Citer

Ernesto Frodden, Marc Geiller, Karim Noui, Alejandro Perez. Statistical Entropy of a BTZ Black Hole from Loop Quantum Gravity. Journal of High Energy Physics, 2013, 2013 (5), pp.139. ⟨10.1007/JHEP05(2013)139⟩. ⟨hal-00957632⟩
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