Thermodynamic curvature of the BTZ black hole - art. no. 067502

In this paper we apply the concept of thermodynamic geometry to the Banados -Teitelboim-Zanelli (BTZ) black hale. We find the thermodynamic curvature d iverges at the extremal limit of the black hole, which means the extremal b lack hole is the critical point with the temperature zero. We also study th e effective dimensionality of the underlying statistical model. Near the cr itical point, the picture is clear; the spatial dimension of the underlying statistical model is just one, which agrees with other results. However, f ar from the critical point, the dimension becomes less than one and even ne gative. In order to interpret this result, we resort to a qualitative analo gy with the Takahashi gas model. [S0556-2821(99)04516-6].