Analysis of exponential corrected thermodynamic geometries in AdS5×S5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$AdS_5\ imes S^5$$\\end{document} black hole

Abstract

This paper delves the thermodynamics of 5-dimensional Schwarzschild AdS5×S5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$AdS_5 \ imes S^5$$\\end{document} black hole by considering the recently proposed effective models of exponential entropies. The conventional understanding of cosmological constant Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} 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 Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} 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 N2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N^2$$\\end{document} 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.