[论文解读] Topology of Born-Infeld-AdS Black Hole Phase Transitions: Bulk and CFT Sides

Md Sabir Ali, H. El Moumni+2 more|arXiv (Cornell University)|Jun 20, 2023

Black Holes and Theoretical Physics参考文献 122被引用 4

一句话总结

本文利用Duan的拓扑规范理论与非壳自由能分析，研究了Born-Infeld-AdS黑洞相变的拓扑结构。研究发现临界点表现为涡旋/反涡旋对，揭示了在某些参数区域内存在拓扑破缺，并发现了不稳定黑洞相之间的一种新型相变，其结果与BKT相变及类似马蹄铁状的热力学行为相类似。

ABSTRACT

The thermodynamic criticality of the AdS black holes serves as an important structure during the thermal phase transition. This paper discusses about the critical points and their topology during thermal phase transitions of the Born-Infeld AdS black holes. We make such investigations using two different topological approaches, namely, using Duan's topological current $ϕ$-mapping theory, and the off-shell free energy. Within Duan's formalism, we observe that for a given value of the Born-Infeld parameter $b$, there exists an associated electric charge parameter $Q$, which is highly sensitive to the topological phase transitions. This way we examine the connections of the first-order phase transition and the topological nature of the critical points. We find that the topological nature has a possible breakdown in certain parametric ranges. In effect, we determine the unconventional and the conventional phase critical points as the creation (topologically vortex) and annihilation (topologically anti-vortex) points (pairs). As the second approach, we call the off-shell free energy to determine the topological classes: of which one corresponds to the AdS-Schwarzschild black hole phases, while the other provides a possible topological phase transition. Here we also reveal a novel phase transition between two unstable phases, namely, the unstable small black hole and the intermediate black holes. For a certain parametric values of the Born-Infeld parameter and the pressure, we also study the different topological descriptions that inevitably correspond to the AdS-Reissner-Nordstr$\Ddot{o}$m black hole phases. As a consistency check of the critical points during the topological phase transitions, we study the vortex/anti-vortex annihilation thermodynamics from local as well as global thermodynamic viewpoint.

研究动机与目标

• 理解Born-Infeld-AdS黑洞相变中临界点的拓扑本质。
• 探讨Born-Infeld参数与电荷对拓扑相变的影响。
• 利用Duan的$φ$-映射理论与非壳自由能，识别并分类拓扑相。
• 分析小、中等与大黑洞相的热力学稳定性与拓扑性质。
• 建立涡旋/反涡旋湮灭与热力学相变之间的对应关系。

提出的方法

• 应用Duan的拓扑规范理论$φ$-映射方法，将Born-Infeld-AdS黑洞中的临界点映射为拓扑缺陷。
• 从吉布斯自由能构造矢量场，以分析拓扑电荷并分类相。
• 利用非壳自由能，确定在不同$Q$与$T$条件下S型与RN型黑洞的拓扑类别。
• 在$(1/Q, T)$平面上绘制涡旋/反涡旋的产生与湮灭点，以模拟热力学马蹄铁行为。
• 通过局域与全局热力学稳定性分析，验证拓扑相变的信号。
• 将结果与已知相变进行比较，包括类似BKT的相变与RN-AdS行为。

实验结果

研究问题

• RQ1 Born-Infeld-AdS黑洞中的临界点如何在拓扑上表现？其作为涡旋或反涡旋对的性质是什么？
• RQ2 Born-Infeld参数$b$在相变过程中对拓扑结构破缺起到何种作用？
• RQ3 非壳自由能能否用于对S型与RN型Born-Infeld-AdS黑洞中的不同拓扑相进行分类？
• RQ4 在黑洞相变背景下，涡旋/反涡旋对的产生与湮灭具有何种热力学意义？
• RQ5 当系统在不稳定黑洞相之间发生转变时，其行为如何变化？何种拓扑特征会显现？

主要发现

• Born-Infeld-AdS黑洞中的临界点在拓扑上被分类为涡旋（产生）与反涡旋（湮灭）对，且在$Q = Q_m$处具有拓扑电荷$\mathcal{Q} = -1$。
• 当$b = 8\pi Q_m$时，拓扑相变结构发生破缺，此后系统行为类似于RN-AdS黑洞，不再具有不稳定相。
• 发现了一种新型相变，存在于不稳定的小黑洞（SSBH）与中间黑洞（IBH）相之间，该现象在标准RN-AdS系统中未被观测到。
• $(1/Q, T)$平面呈现出类似马蹄铁的结构，与一级相变类似，LBH/SSBH湮灭与SSBH产生过程具有不同的热力学行为。
• 局域与全局热力学分析证实，涡旋/反涡旋湮灭与热力学稳定性及自由能行为一致。
• 当$Q < Q_m$时，吉布斯自由能呈现尖点状结构并表现出Hawking-Page类似相变；而当$Q > Q_m$时，无此类尖点出现，表明存在拓扑与热力学上的差异。