Black hole geometrothermodynamics and critical phenomena: a look from Tsallis entropy-based perspective

TL;DR

This paper explores how Tsallis non-additive entropy influences the thermodynamic geometry and phase transitions of charged AdS black holes and BTZ black holes, revealing non-trivial effects on their critical behavior and analogy with van der Waals fluids.

Contribution

It introduces the application of Tsallis entropy to black hole thermodynamics, analyzing its impact on phase transitions, critical exponents, and thermodynamic curvature within a geometric framework.

Findings

Tsallis entropy affects black hole phase transition behavior.

Thermodynamic curvature reveals non-trivial geometric effects.

Modified critical exponents suggest new universality features.

Abstract

We analyze geometrothermodynamics of charged anti-de Sitter (AdS) black holes with a global monopole in the framework of Tsallis statistics. The latter arises from a non-additive generalization of Boltzmann-Gibbs entropy, which is still recovered as a particular sub-case. We examine the effects of Tsallis entropy on small-large black holes phase-transitions and critical exponents, comparing the results with the liquid-gas change of phase occurring in van der Waals fluids. We also discuss some physical constraints on Tsallis parameter and the impact on sparsity of BH radiation. Thermodynamic curvature behavior is then explored from a geometric perspective within Ruppeiner formalism on the $S-P$ coordinate space. Similar considerations are extended to charged $(2+1)$-dimensional Banados-Teitelboim-Zanelli (BTZ) black holes by computing the entropy-pressure and entropy volume corrected curvatures. Our analysis shows that Tsallis prescription has non-trivial implications on black hole geometrothermodynamics, emphasizing the role of non-additive entropy on the correspondence between black holes and van der Waals systems.