1212.4060 (Ernesto Frodden et al.)

Black Hole Entropy from complex Ashtekar variables    [PDF]

Ernesto Frodden, Marc Geiller, Karim Noui, Alejandro Perez

In loop quantum gravity, the number $N_\Gamma(a_H,\gamma)$ 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 $N_\Gamma(a_H,\pm i)$ of microstates behaves as $\exp(a_H/(4\lp^2))$ for large area $a_H$ 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.

View original: http://arxiv.org/abs/1212.4060