Entropy of Isolated Horizons revisited

Details Entropy of Isolated Horizons revisited Entropy of Isolated Horizons revisited

2009-07-05

arxiv.org/abs/0907.0846v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 Pages Latex, no figures; penultimate paragraph on invariance of equations satisfied by IH states, under action of Gauss law

Scientific paper

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.

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