Entropy of isolated horizons revisited

The decade-old formulation of the isolated horizon classically and within loop quantum gravity, and the extraction of the microcanonical entropy of such a horizon from this formulation, is reviewed, in view of recent renewed interest. There are two main approaches to this problem: one employs an $SU(2)$ Chern-Simons theory describing the isolated horizon degrees of freedom, while the other uses a reduced $U(1)$ Chern-Simons theory obtained from the $SU(2)$ theory, with appropriate constraints imposed on the spectrum of boundary states “living” on the horizon. It is shown that both these ways lead to the same infinite series asymptotic in the horizon area for the microcanonical entropy of an isolated horizon. The leading area term is followed by an unambiguous correction term logarithmic in area with a coefficient $-\frac{3}{2}$, with subleading corrections dropping off as inverse powers of the area.