Phase transitions and structure of 5D AdS black holes immersed in Chaplygin-like dark fluid from Kaniadakis statistics

Motivated by the recently exploited concept of Kaniadakis entropy, we construct a five-dimensional spherically symmetric static black hole (BH) solution surrounded by dark fluid with a Chaplygin-like equation of state $p=-\gamma /\rho$ (CDF) in anti-de Sitter space (AdS). Conventionally speaking, Boltzmann entropy-based thermodynamics of charged AdS black holes (BHs) have been shown to display physically interesting features, viz., P–v criticalities and van der Waals-type BHs. This work highlights the extended version of the standard Boltzmann entropy, i.e., Kaniadakis entropy, which is a non-extensive generalization of classical statistical mechanics. Borrowing ideas from the condensed matter physics realm, we assess the impact of Kaniadakis entropy on the P–v critical study, Gibbs free energy, and critical exponents of five-dimensional AdS BHs with CDF background in the extended phase space. A particular interest is concerned with the exploitation of geothermodynamics tools, especially Hendi, Panahiyan, Eslam Panah, and Momennia (HPEM) geometry. This offers the possibility of predicting physical limitations and physical transition points. Our analysis breaks new ground in the understanding of BH thermodynamics in a relativistic statistical framework, emphasizing the role of non-extensive corrections in the dual AdS BH/Van der Waals fluid pattern.