Thermodynamic Signatures and Insights into Horava–Lifshitz AdS Black Holes

In this work, we study some aspects of thermodynamic universality, topology, and geometry of charged anti–de Sitter (AdS) black holes within the framework of Horava-Lifshitz gravity. The universal relation is established, demonstrating how the weak gravity conjecture manifests within the thermodynamic behavior of these black holes. Further, by employing vector field analysis, the distribution and stability of topological charges are examined, and some points corresponding to localized charge structures are identified, revealing that the total topological charge remains conserved despite variations in system parameters. The results are consistent with standard black hole classifications, confirming the robustness and reliability of the topological framework. Next, we compute thermodynamic curvature and phase behavior, which reveals a transition in the dominant microscopic interactions governing the black hole microstructures from repulsive to attractive type interactions. This transition occurs, indicating that modifications in gravity and charge play crucial roles in shaping interactions among the microstructures. Furthermore, the photon sphere structure is investigated and shown to exhibit topological invariance under continuous parameter variations, providing an additional means of characterizing the system.