Analytic continuation of the rotating black hole state counting

In loop quantum gravity, a spherical black hole can be described in terms of a chern-simons theory on a punctured 2-sphere. the sphere represents the horizon. the punctures are the edges of spin-networks in the bulk which cross the horizon and carry quanta of area. one can generalize this construction and model a rotating black hole by adding an extra puncture colored with the angular momentum j in the 2-sphere. we compute the entropy of rotating black holes in this model and study its semi-classical limit. after performing an analytic continuation which sends the barbero-immirzi parameter to γ = ±i,weshowthattheleadingorderterminthesemi-classicalexpansionoftheentropy reproduces the bekenstein-hawking law independently of the value of j.