Effects of Exponential Entropy on Thermodynamic Geometries

Abstract

This thesis delves into the analysis of thermodynamics of a 5-D Schwarz- schild AdS black hole(BH) within the AdS5 £ S5 spacetime, incorporatingexponential entropies. The conventional understanding of ¤ (cosmological constant) as thermodynamic pressure, with volume being its counterpart, cannot be directly applied in the framework of the AdS/CFT correspon- dence. Instead, we establish a connection between the ¤ in the boundary gauge theory and N (number of colors), where the thermodynamic conju- gate is represented by the chemical potential. In this study, we replace the geometric parameters L and r of the AdS black hole with two thermody-namic parameters N 2 and S in the micro canonical ensemble. Additionally, we valuate various formulations of thermodynamic geometry, such as Rup- peiner, Quevedo and Weinhold, and derive the associated scalar curvatures for the 5-D Schwarzschild AdS BH. We see these geometries exhibit attrac- tion/repulsion forces on particles.