EDGE STATES AND ENTROPY OF 2-DIMENSIONAL BLACK-HOLES

In several recent publications Carlip, as well as Balachandran, Chanda r, and Momen, has 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 d iscussing several routes for deriving a boundary action, we examine th eir hypothesis in the context of generic 2D dilaton gravity. We first calculate the corresponding statistical-mechanical entropy of black ho les in 1+1 de Sitter 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 facil itated greatly by the Poisson sigma-model formulation of these theorie s. It turns out that the phase space of the boundary particles coincid es precisely with a symplectic leaf of the Poisson manifold that enter s as target space of the sigma model. Despite this qualitatively appea ling picture, the quantitative results are discouraging: In most of th e cases, the symplectic leaves are noncompact and the number of micros tates yields a meaningless infinity. In those cases where the particle phase space is compact-such as, e.g., in the Euclidean de Sitter theo ry-the edge state degeneracy is finite, but generically it is far too small to account for the semiclassical Bekenstein-Hawking entropy.