Entropy of Isolated Horizons revisited

TL;DR

This paper reviews the entropy calculation of isolated horizons in loop quantum gravity, comparing SU(2) and U(1) approaches, and confirms a universal logarithmic correction term with coefficient -3/2.

Contribution

It demonstrates the equivalence of SU(2) and U(1) Chern-Simons approaches in deriving horizon entropy and clarifies the correction terms in the entropy-area relation.

Findings

Both approaches yield the same asymptotic entropy series.

The leading correction is a logarithmic term with coefficient -3/2.

Subleading corrections decrease as inverse powers of area.

Abstract

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.