热分析、焦耳-汤姆逊膨胀和霍金稀疏性：浸没在弦云中的Mod(A)Max-AdS黑洞
Thermal Analysis, Joule-Thomson Expansion and Hawking Sparsity of Mod(A)Max-AdS Black Hole Immersed in a Cloud of Strings
AI总结：
本文研究了浸没在弦云中的Mod(A)Max-AdS黑洞的热力学行为，探讨了其稳定性、相变及霍金辐射稀疏性，揭示了模型参数对相结构和辐射特性的影响。
摘要：
我们研究了一个被弦云包围的球对称反德西特黑洞在Mod(A)Max电动力学中的热力学行为。在扩展相空间框架内，我们将宇宙学常数视为压力，并将黑洞质量解释为焓，这使得可以统一讨论局部稳定性、全局相结构和焦耳-汤姆逊膨胀。我们分析了霍金温度、吉布斯自由能和热容，并展示了弦云参数、Mod(A)Max变形和电荷如何重塑物理域、稳定性窗口以及小/大黑洞转变模式。我们进一步表征了临界行为，并证明只有在物理部分会出现类似范德瓦尔斯的相结构，而替代分支不承认真正的临界点。对于焦耳-汤姆逊过程，我们确定了逆曲线和相应的等焓轨迹，突显了模型参数如何控制冷却/加热区域，并且在足够大的电荷下可以产生终止的等焓行为。最后，我们检查了霍金辐射的稀疏性，并讨论了底层参数如何影响发射流的时间离散性，特别是在极端性和大半径AdS区域附近。
英文摘要：
We investigate the thermodynamic behavior of a spherically symmetric Anti-de Sitter black hole in Mod(A)Max electrodynamics surrounded by a cloud of strings. Within the extended phase-space framework, we treat the cosmological constant as a pressure and interpret the black-hole mass as enthalpy, which enables a unified discussion of local stability, global phase structure, and Joule--Thomson expansion. We analyze the Hawking temperature, Gibbs free energy, and heat capacity, and show how the string-cloud parameter, the Mod(A)Max deformation, and the electric charge reshape the physical domain, the stability windows, and the small/large black-hole transition pattern. We further characterize the critical behavior and demonstrate that a van der Waals--like phase structure arises only in the physical sector, while the alternate branch does not admit a genuine critical point. For the Joule-Thomson process, we determine the inversion curve and the corresponding isenthalpic trajectories, highlighting how the model parameters control the cooling/heating regimes and can generate terminating isenthalpic behavior at sufficiently large charge. Finally, we examine the sparsity of Hawking radiation and discuss how the underlying parameters influence the temporal discreteness of the emitted flux, particularly near extremality and in the large-radius AdS regime.
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