Thermodynamic Curvature of the BTZ Black Hole

Details Thermodynamic Curvature of the BTZ Black Hole Thermodynamic Curvature of the BTZ Black Hole

1998-03-31

arxiv.org/abs/hep-th/9803261v1

Phys.Rev. D60 (1999) 067502

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, LaTeX with revtex macro, 4 figures in eps files

Scientific paper

10.1103/PhysRevD.60.067502

Some thermodynamic properties of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole are studied to get the effective dimension of its corresponding statistical model. For this purpose, we make use of the geometrical approach to the thermodynamics: Considering the black hole as a thermodynamic system with two thermodynamic variables (the mass $M$ and the angular momemtum $J$), we obtain two-dimensional Riemannian thermodynamic geometry described by positive definite Ruppeiner metric. From the thermodynamic curvature we find that the extremal limit is the critical point. The effective spatial dimension of the statistical system corresponding to the near-extremal BTZ black holes is one. Far from the extremal point, the effective dimension becomes less than one, which leads to one possible speculation on the underlying structure for the corresponding statistical model.

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