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# Black-hole entropy from complex Ashtekar variables

Abstract : In loop quantum gravity, the number $N_\Gamma(A,\gamma)$ of microstates of a black hole for a given discrete geometry $\Gamma$ depends on the so-called Barbero-Immirzi parameter $\gamma$. Using a suitable analytic continuation of $\gamma$ to complex values, we show that the number $N_\Gamma(A,\pm i)$ of microstates behaves as $\exp(A/(4\ell_\text{Pl}^2))$ for large area $A$ in the large spin semiclassical limit. Such a correspondence with the semiclassical Bekenstein-Hawking entropy law points towards an unanticipated and remarkable feature of the original complex Ashtekar variables for quantum gravity.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00957634
Contributor : Alejandro Perez Connect in order to contact the contributor
Submitted on : Monday, March 10, 2014 - 4:57:29 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:08 PM

### Citation

E. Frodden, M. Geiller, K. Noui, A. Perez. Black-hole entropy from complex Ashtekar variables. EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2014, 107 (1), ⟨10.1209/0295-5075/107/10005⟩. ⟨hal-00957634⟩

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