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arXiv · 1212.4060

Black Hole Entropy from complex Ashtekar variables

Ernesto Frodden·Marc Geiller·Karim Noui·Alejandro Perez
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Abstract

In loop quantum gravity, the number $N_Γ(A,γ)$ of microstates of a black hole for a given discrete geometry $Γ$ depends on the so-called Barbero-Immirzi parameter $γ$. Using a suitable analytic continuation of $γ$ to complex values, we show that the number $N_Γ(A,\pm i)$ 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.

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Ernesto Frodden, Marc Geiller, Karim Noui, Alejandro Perez. 2013-12-28. Black Hole Entropy from complex Ashtekar variables. https://doi.org/10.1209/0295-5075%2F107%2F10005

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