Holographic and Thermodynamic Topological Perspectives on AdS Einstein-Power-Yang-Mills Black Holes with Generalized Entropy

In this work, we explore the holographic and thermodynamic topology of Anti–de Sitter (AdS) Einstein–Power–Yang–Mills (EPYM) black holes using both the bulk–boundary correspondence and the restricted phase space (RPS) frameworks. The study employs several non-extensive entropy models, including Barrow, R´enyi, Sharma–Mittal, Kaniadakis, and Tsallis–Cirto entropies. Within the bulk–boundary formalism, we find that the free deformation parameters strongly influence the classification of topo logical charges w. For the Barrow entropy, two distinct topological charges w = +۱ and w = −۱ appear as the deformation parameter increases, closely resembling the Bekenstein–Hawking limit. The R´enyi entropy exhibits a transition from three charges w = (+۱, ۰, −۱) to a single charge w = +۱ as the non-extensive parameter rises, while setting the deformation parame ter to zero yields two symmetric charges w = ±۱. In the Sharma–Mittal framework, three characteristic regions emerge: for higher parameter ra tios, w = +۱; for balanced ratios, w = ۰; and for lower ratios, w = −۱. The Kaniadakis entropy generally shows w = ±۱ for most admissible K values, except at K = ۰, where only w = +۱ remains. The Tsallis–Cirto entropy displays two topological charges w = ±۱ for small deformation parameters and a single charge w = +۱ as the parameter approaches ۰.۹. Extending the analysis to the RPS framework reveals that, for R´enyi, Sharma–Mittal, and Tsallis–Cirto entropies, the topological charge remains invariant at w = +۱, regardless of parameter variation. However, in the Barrow and Kaniadakis cases, the topological configuration evolves with increasing non extensivity, leading to distinct topological transitions in w. These findings provide deeper insights into the holographic and thermodynamic structure of non-extensive AdS black holes and highlight their phase evolution under generalized entropy formulations. The present work differs by (i) an explicit bulk boundary holographic mapping that tracks how the EPYM power q modifies boundary central-charge and chemical potential variables, (ii) ad ditional analytic expansions and parameter-range scans for q and entropy deformation parameters, and (iii) the introduction of supplementary stabil ity diagnostics and response-function tests that probe the robustness of the topology classification.

کلیدواژه ها:

Holography ، thermodynamic ، Black Holes ، topology