Analytic continuation of the rotating black hole state counting
Résumé
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.
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