Geometric Thermodynamics of Well-Known Black Holes

Abstract

We study the phase transition and thermodynamic geometries of a charged AdS black hole with a global monopole. For this purpose, we develop the thermodynamic quantities such as Hawking temperature, spe- cific heat and pressure on horizon radius in the presence of Barrow entropy. The stability of this black hole is being observed through specific heat. Also, we investigate the thermodynamic curvatures behavior of black hole by applying Weinhold and Ruppiner formulations. It is found that ther- modynamic curvatures exhibit the attractive and repulsive nature of black hole for specific constants. We also study the thermodynamic curvature of charged BTZ black hole by fixing phase space of entropy, pressure and volume on curvature, i.e., entropy-pressure corrected curvature (RSP ) and entropy-volume corrected curvature (RSV ). It is found that there present a repulsive force by the charged BTZ black hole for its molecules, qual- itatively or phenomenologically. However, RSV shows negative behavior initially which exhibits the attractive nature of charged BTZ black hole.