Effects of Modified Entropies on Geometric Thermodynamics of Black Holes

Abstract

In this thesis, we analyze the thermodynamics of five-dimensional Schwarz- schild AdS black hole in AdS5 × S5 spacetime in the presence of Tsallis entropy. Since the cosmological constant Λ is considered as thermodynam- ical pressure with volume as its conjugate, but this explanation cannot be employed in AdS/CFT correspondence. In this study, we associate cosmo- logical constant Λ in boundary Gauge theory with the number of colors N and chemical potential is taken to be its thermodynamic conjugate. The two geometric parameters in the AdS black hole, r and L are substituted for two thermodynamic parameters in the micro-canonical ensemble, which are considered to be entropy S and N2. Moreover, we evaluate several thermodynamical geometry formulations, including Weinhold, Ruppeiner, and Quevedo and derive associated scalar curvatures for five-dimensional Schwarzschild AdS black hole