https://doi.org/10.1140/epjc/s10052-023-12203-5
Regular Article - Theoretical Physics
Analysis of exponential corrected thermodynamic geometries in 
black hole
1
Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology, 310023, Hangzhou, China
2
Department of Mathematics, COMSATS University Islamabad, Lahore-Campus, 54000, Lahore, Pakistan
3
Department of Natural Sciences and Humanities, University of Engineering and Technology, New Campus, KSK, Lahore, Pakistan
a shamtoor181@outook.com, drshamailarani@cuilahore.edu.pk
Received:
23
September
2023
Accepted:
23
October
2023
Published online:
19
November
2023
This paper delves the thermodynamics of 5-dimensional Schwarzschild 
black hole by considering the recently proposed effective models of exponential 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 correspondence. In order to resolve this issue, we establish a connection between the cosmological constant 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 
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.
© The Author(s) 2023
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
