Black Hole Entropy and SU(2) ChernSimons Theory
Abstract
Black holes (BH’s) in equilibrium can be defined locally in terms of the socalled 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 ChernSimons 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 ∆S=(3)/(2)loga_{H}. Our treatment from first principles settles previous controversies concerning the counting of states.
 Publication:

Physical Review Letters
 Pub Date:
 July 2010
 DOI:
 10.1103/PhysRevLett.105.031302
 arXiv:
 arXiv:0905.3168
 Bibcode:
 2010PhRvL.105c1302E
 Keywords:

 04.70.Dy;
 04.60.Pp;
 Quantum aspects of black holes evaporation thermodynamics;
 Loop quantum gravity quantum geometry spin foams;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 Final form, to appear in Phys. Rev. Lett. Some extra details on the constraint algebra added, some details on the quantization have been omitted to comply with PRL length standards (they appear however in arXiv:1006.0634)