Thermodynamic Geometry of Normal (Exotic) BTZ Black Hole Regarding to the Fluctuation of Cosmological Constant

Abstract

We construct the thermodynamic geometry of $2+1$ dimensional normal (exotic) BTZ black hole regarding to the fluctuation of cosmological constant. We argue that while the thermodynamic geometry of black hole without fluctuation of cosmological constant is a two dimensional flat spaces, the three dimensional thermodynamics parameters space including the cosmological constant as a fluctuating parameter will be curved. Some consequence of the fluctuation of cosmological constant will be investigated. We show that such fluctuation leads to a thermodynamics curvature which is correctly singular at critical surface of the system. Also, we consider the validity of first thermodynamics law regarding to the fluctuation of cosmological constant.