Analysis of exponential corrected thermodynamic geometries in $$AdS_5\times S^5$$ A d S 5 × S 5 black hole

Abstract

Abstract This paper delves the thermodynamics of 5-dimensional Schwarzschild $$AdS_5 \times S^5$$ A d S 5 × S 5 black hole by considering the recently proposed effective models of exponential entropies. The conventional understanding of cosmological constant $$\Lambda $$ Λ as thermodynamic pressure with volume being its counterpart cannot be directly applied in the framework of the AdS/CFT correspondence. In order to resolve this issue, we establish a connection between the cosmological constant $$\Lambda $$ Λ in the boundary gauge theory and number of colors N while chemical potential is considered as thermodynamic conjugate. In this study, we replace the geometric parameters L and r of the AdS black hole with two thermodynamic parameters $$N^2$$ N 2 and S in the micro-canonical ensemble. Additionally, we explore the various thermodynamic geometry models such as Ruppeiner, Quevedo and Weinhold to derive the associated scalar curvatures for the 5-D Schwarzschild AdS BH. We analyze that these geometries exhibit microscopic attraction/repulsion forces on the particles of black hole.