2026/07/15 by Yu-Die Wan, Peng Zhao, Zheng-Wen Long
#gr-qc
Based on the ϕ-mapping topological current theory, we systematically investigate the thermodynamic topology of regular Bardeen-AdS-class black holes coupled to nonlinear electrodynamics, a class of singularity-free geometries whose topological classification remains underexplored. We implement numerical calculations at two typical AdS radii L=1 and L=15. Within the fundamental W0- topological family, we identify a novel inner secondary subclass \widetildeW0-. This result only refines and enriches the internal branch structure of the W0- family under the established classification scheme of five topological classes and four topological subclasses for black hole thermodynamics. This new subclass has a vanishing global topological charge W=0 with an inner-outer horizon winding-number signature [-,+]. Unlike standard W0- solutions that realize topological extension via embedded (+,-) winding pairs, \widetildeW0- arises from attaching an extra stable branch to the end of the base solution sequence. Two critical coupling parameters m01 and m02 divide the full parameter space into distinct topological phases: Type I black holes with m0≥m01 and Type II solutions with m02<m0<m01 belong to \widetildeW0-, while the parameter region 0<m0≤m02 corresponds to the conventional W0- topology. Our numerical results verify the self-consistency of the thermodynamic topological formalism when applied to singularity-free regular black holes, refine the topological discrimination criteria tailored to nonlinear-electrodynamics regular black holes, and provide theoretical references for subsequent topological investigations of higher-dimensional rotating regular black holes under the same formalism.