AI 中文总结
基于黑洞热容量提出拓扑框架，构建二维矢量场，用布劳威尔度表征临界点拓扑，应用于反德西特黑洞解，证明有全局守恒拓扑电荷，揭示拓扑转变机制，为黑洞热力学多临界点研究提供统一框架。
AI 中文摘要
在本论文中，我们基于黑洞的热容量提出了一个新颖的拓扑框架来研究热力学多临界点的拓扑结构。我们构建了一个二维热力学矢量场，其孤立零点对应于系统的临界点。每个临界点的局部拓扑由其布劳威尔度表征，它是一个局部守恒的拓扑量。将此形式体系应用于几个反德西特黑洞解，我们证明每个系统都具有一个全局守恒的拓扑电荷。尽管热力学临界点数量随热力学参数变化，但总拓扑电荷在整个演化过程中保持不变。我们表明这些拓扑转变由携带相反布劳威尔度的拓扑中性缺陷对的产生或湮灭所支配。我们的结果为理解黑洞系统中热力学多临界点的出现、演化和分类提供了一个统一的拓扑框架。
英文摘要
In this manuscript, we propose a novel topological framework based on the heat capacity of black holes to investigate the topology of thermodynamic multicritical points. We construct a two-dimensional thermodynamic vector field whose isolated zeros correspond to the critical points of the system. The local topology of each critical point is characterized by its Brouwer degree, which serves as a locally conserved topological quantity. Applying this formalism to several AdS black hole solutions, we demonstrate that each system possesses a globally conserved topological charge. Although the number of thermodynamic critical points changes as the thermodynamic parameters are varied, the total topological charge remains invariant throughout the evolution. We show that these topological transitions are governed by the creation or annihilation of topologically neutral defect pairs carrying opposite Brouwer degrees. Our results provide a unified topological framework for understanding the emergence, evolution, and classification of thermodynamic multicritical points in black hole systems.
Comments21 pages, 14 figures
