Study of Thermal Stability and Thermodynamic Geometries of Well-Known Black Holes through Entropy Corrections

Abstract

In this thesis, we investigate the thermal stability and thermodynamic geometries of non-rotating/rotating charged black holes. For these black holes, we apply Barrow and power-law entropy to determine the physical quantities such as mass and temperature of the system and ¯nd their sta- bility through ¯rst and second phase transitions of the heat capacity. We analyze the e®ects of scalar charge Q and hair parameter ¸ on black holes properties by taking both positive and negative values of these parame- ters. It is noted that heat capacity provide the stable, unstable regions and phase transition points for both black holes. To investigate the thermody- namic geometry of these black holes, various techniques such as Ruppeiner, Weinhold, Quevedo and HPEM metrics are considered. It is observed that Weinhold, Quevedo and HPEM give attrative/repulsive behavior of parti- cles in stable/unstable regions of black holes.