Edge States and Entropy of 2d Black Holes

TL;DR

This paper investigates the statistical mechanical interpretation of black hole entropy via boundary degrees of freedom in 2D dilaton gravity, finding that the microstate count often diverges or is too small to match classical entropy.

Contribution

It extends boundary state analysis to generic 2D dilaton gravity, including non-gauge theories, and critically assesses their role in black hole entropy.

Findings

In 1+1 deSitter gravity, boundary microstates match entropy calculations.

Most cases yield infinite or negligible microstate counts, challenging the boundary interpretation.

Finite microstates in some models are insufficient to explain Bekenstein-Hawking entropy.

Abstract

In several recent publications Carlip, as well as Balachandran, Chandar and Momen, have proposed a statistical mechanical interpretation for black hole entropy in terms of ``would be gauge'' degrees of freedom that become dynamical on the boundary to spacetime. After critically discussing several routes for deriving a boundary action, we examine their hypothesis in the context of generic 2-D dilaton gravity. We first calculate the corresponding statistical mechanical entropy of black holes in 1+1 deSitter gravity, which has a gauge theory formulation as a BF-theory. Then we generalize the method to dilaton gravity theories that do not have a (standard) gauge theory formulation. This is facilitated greatly by the Poisson-Sigma-model formulation of these theories. It turns out that the phase space of the boundary particles coincides precisely with a symplectic leaf of the Poisson manifold that enters as target space of the Sigma-model. Despite this qualitatively appealing picture, the quantitative results are discouraging: In most of the cases the symplectic leaves are non-compact and the number of microstates yields a meaningless infinity. In those cases where the particle phase space is compact - such as, e.g., in the Euclidean deSitter theory - the edge state degeneracy is finite, but generically it is far too small to account for the semiclassical Bekenstein-Hawking entropy.