Abstract
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 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 , the counting can be mapped to simply counting the number of intertwiners compatible with the spins labeling the punctures. The resulting BH entropy is proportional to with logarithmic corrections . Our treatment from first principles settles previous controversies concerning the counting of states.
- Received 14 September 2009
DOI:https://doi.org/10.1103/PhysRevLett.105.031302
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