Thermodynamics of rotating AdS black holes in Kaniadakis statistics

In this study, we investigate the thermodynamic properties and phase transitions in rotating anti-de Sitter (AdS) black holes by applying the Kaniadakis (KD) entropy framework. To achieve this, we analyze three prominent rotating AdS black hole systems: the Kerr AdS black hole, the Kerr-Sen AdS black hole, and the Kerr–Newman AdS black hole. We assess their thermodynamic quantities, phase transitions, thermodynamic topology and thermodynamic geometry within the Kaniadakis statistical framework. We observed that Kaniadakis entropy introduces an entropy bound beyond which the black hole solutions become thermally unstable, unlike the Gibbs–Boltzmann framework, where stability persists across infinite Bekenstein–Hawking entropy range. This bound is controlled by the Kaniadakis parameter $\kappa$, with smaller $\kappa$ values allowing stability over a broader entropy range. To illustrate these changes, we examine the free energy landscape, which highlights alterations in the phase structure and the stability of black holes. Thermodynamic topology further indicates that the topological class of these black holes changes from 1 to 0 when transitioning from GB to KD statistics. Along with changes in the topological charge, the number of creation and annihilation points also changes. Notably, the topological charge remains independent of all thermodynamic parameters in both GB and KD statistics. We discuss the thermodynamic geometry of rotating AdS black holes using two different formalisms: Ruppeiner and Geometrothermodynamic (GTD). Our analysis uncovers unequal number of singularities in the scalar curvature within both frameworks. In the Ruppeiner formalism, these singularities do not coincide with the discontinuities observed in the heat capacity curves. In contrast, the GTD formalism shows that the singularities in the scalar curvature align with the discontinuities in the heat capacity curves.