Black hole entropy from the SU(2)-invariant formulation of type I isolated horizons

30 pages, 1 figureInternational audienceA detailed analysis of the spherically symmetric isolated horizon system is performed in terms of the connection formulation of general relativity. The system is shown to admit a manifestly SU(2) invariant formulation where the (effective) horizon degrees of freedom are described by an SU(2) Chern-Simons theory. This leads to a more transparent description of the quantum theory in the context of loop quantum gravity and modifications of the form of the horizon entropy