AI 中文总结
研究巴丁-反德西特类黑洞的热力学拓扑，基于φ映射拓扑电流理论，通过数值计算在特定反德西特半径下，于W⁰⁻拓扑族中识别出新子类W⁰⁻，划分拓扑相，验证形式主义自洽性，细化判别标准并提供理论参考。
AI 中文摘要
基于φ映射拓扑电流理论，我们系统地研究了与非线性电动力学耦合的正则巴丁-反德西特类黑洞的热力学拓扑，这是一类拓扑分类尚未充分探索的无奇点几何。我们在两个典型的反德西特半径L = 1和L = 15处进行了数值计算。在基本的W⁰⁻拓扑族中，我们识别出一个新的内部次子类W⁰⁻。这一结果仅在既定的黑洞热力学五拓扑类和四拓扑子类分类方案下，细化和丰富了W⁰⁻族的内部分支结构。这个新子类的全局拓扑电荷W = 0，具有内外视界缠绕数特征[-，+]。与通过嵌入(+，-)缠绕对实现拓扑扩展的标准W⁰⁻解不同，W⁰⁻是通过在基解序列末尾附加一个额外的稳定分支产生的。两个临界耦合参数m₀₁和m₀₂将整个参数空间划分为不同的拓扑相：m₀≥m₀₁的I型黑洞和m₀₂<m₀<m₀₁的II型解属于W⁰⁻，而参数区域0<m₀≤m₀₂对应于传统的W⁰⁻拓扑。我们的数值结果验证了热力学拓扑形式主义应用于无奇点正则黑洞时的自洽性，细化了针对非线性电动力学正则黑洞的拓扑判别标准，并为同一形式主义下高维旋转正则黑洞的后续拓扑研究提供了理论参考。
英文摘要
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 $W^{0-}$ topological family, we identify a novel inner secondary subclass $\widetilde{W}^{0-}$. This result only refines and enriches the internal branch structure of the $W^{0-}$ 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 $W^{0-}$ solutions that realize topological extension via embedded $(+,-)$ winding pairs, $\widetilde{W}^{0-}$ arises from attaching an extra stable branch to the end of the base solution sequence. Two critical coupling parameters $\hat{m}_{01}$ and $\hat{m}_{02}$ divide the full parameter space into distinct topological phases: Type I black holes with $m_0\ge\hat{m}_{01}$ and Type II solutions with $\hat{m}_{02}<m_0<\hat{m}_{01}$ belong to $\widetilde{W}^{0-}$, while the parameter region $0<m_0\le\hat{m}_{02}$ corresponds to the conventional $W^{0-}$ 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.
