Anyon Black Holes

TL;DR

This paper establishes a correspondence between an Anyon Van der Waals fluid and a (2+1)D AdS black hole, revealing how intermediate statistics influence black hole thermodynamics and existence.

Contribution

It introduces a novel AdS black hole solution linked to an Anyon Van der Waals fluid, highlighting the role of intermediate statistics in black hole thermodynamics.

Findings

Black hole thermodynamics matches the fluid's properties.

Existence of black holes depends on the statistics parameter and cosmological constant.

For certain parameters, only quasi Bose-Einstein statistics black holes exist.

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.