Entropy of Isolated Horizons revisited

Understand

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 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 $-\frac32$, with subleading corrections dropping off as inverse powers of the area.