Thermodynamic scalar curvature and topological classification in accelerating charged AdS black holes under rainbow gravity

Abstract

This work investigates the thermodynamic topology of accelerating charged Anti-de Sitter (AdS) black holes within the framework of Rainbow Gravity. By examining vector field configurations, we identify distinct zero points that correspond to localized topological charges. These topological characteristics remain globally conserved under variations of physical parameters, highlighting the robustness of the system's topological structure-closely resembling the behavior seen in AdS Reissner-Nordstr & ouml;m black holes. The acceleration parameter is shown to play a decisive role in shaping these configurations. In addition, the extended thermodynamic formalism is applied to construct a geometric description in the entropy-pressure (S, P) plane, allowing microscopic interactions to be characterized through scalar curvature analysis. This thermodynamic curvature effectively encodes stability properties and phase transitions, distinguishing between attractive and repulsive interactions within the black hole microstructure. Overall, the findings provide new insights into the microstructure, stability, and phase behavior of black holes, clarifying the interplay between acceleration and Rainbow Gravity effects.