Anyon Black Holes

Abstract

We propose a correspondence between an Anyon Van der Waals fluid and a (2+1) dimensional AdS black hole. Anyons are particles with intermediate statistics that interpolates between a Fermi-Dirac statistics and a Bose-Einstein one. A parameter $\alpha$ ($0<\alpha<1$) characterizes this intermediate statistics of Anyons. The equation of state for the Anyon Van der Waals fluid shows that it has a quasi Fermi-Dirac statistics for $\alpha > \alpha_c$, but a quasi Bose-Einstein statistics for $\alpha< \alpha_c$. By defining a general form of the metric for the (2+1) dimensional AdS black hole and considering the temperature of the black hole to be equal with that of the Anyon Van der Waals fluid, we construct the exact form of the metric for a (2+1) dimensional AdS black hole. The thermodynamic properties of this black hole is consistent with those of the Anyon Van der Waals fluid. For $\alpha< \alpha_c$, the solution exhibits a quasi Bose-Einstein statistics. For $\alpha > \alpha_c$ and a range of values of the cosmological constant, there is, however, no event horizon so there is no black hole solution. Thus, for these values of cosmological constants, the AdS Anyon Van der Waals black holes have only quasi Bose-Einstein statistics.Comment: 7 pages, 4 figure