Black hole entropy and $SU(2)$ Chern-Simons theory
Résumé
Black holes (BH’s) in equilibrium can be defined locally in terms of the so-called isolated horizon boundary condition given on a null surface representing the event horizon. We show that this boundary condition can be treated in a manifestly SU(2) invariant manner. Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with punctures. Remarkably, when considering an ensemble of fixed horizon area $a_H$, the counting can be mapped to simply counting the number of SU(2) intertwiners compatible with the spins labeling the punctures. The resulting BH entropy is proportional to $a_H$ with logarithmic corrections $\Delta S$$=$$-$$\frac {3}{2}$ log$a_H$. Our treatment from first principles settles previous controversies concerning the counting of states.
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Licence : CC BY - Paternité
Licence : CC BY - Paternité