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

We analyze geometrothermodynamics of charged anti-de Sitter (AdS) black holes (BHs) with a global monopole in the framework of Tsallis statistics, a non-additive generalization of Boltzmann-Gibbs entropy that recovers the standard case when δ → 1. We study how Tsallis entropy affects small-large BH phase transitions, critical points and exponents, comparing with van der Waals fluids. We also discuss physical constraints on the Tsallis parameter δ and the impact on the sparsity of BH radiation. Using Ruppeiner geometry on the S − P space we explore thermodynamic curvature. We extend the analysis to charged (2+1)-dimensional BTZ black holes, computing entropy-pressure and entropy-volume corrected curvatures. Tsallis prescription yields non-trivial implications for BH geometrothermodynamics and reinforces the BH–van der Waals correspondence under non-additive entropy.