Tsallis entropy inspires geometric thermodynamics of specific black hole

Abstract

Abstract In this paper, we analyze the thermodynamics of five-dimensional Schwarzschild AdS black hole in $$AdS_5 \times S^5$$ A d S 5 × S 5 spacetime in the presence of Tsallis entropy. Since the cosmological constant $$\Lambda $$ Λ is considered as thermodynamical pressure with volume as its conjugate, but this explanation cannot be employed in AdS/CFT correspondence. In this study, we associate cosmological constant $$\Lambda $$ 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 $$N^2$$ N 2 . Moreover, we evaluate several thermodynamical geometry formulations, including Weinhold, Ruppeiner, and Quevedo and derive associated scalar curvatures for five-dimensional Schwarzschild AdS black hole. It is suggested that all these geometries show repulsive/attractive forces on the particles at different phases of entropy.