通过Tsallis统计力学研究黑洞热力学及通过光学特性探测相变
Black Hole Thermodynamics via Tsallis Statistical Mechanics and Phase Transitions Probed by Optical Characteristics
AI总结：
本文基于Tsallis统计力学构建非广延热力学框架，研究Reissner-Nordström黑洞的相变行为，通过光学特性与热力学变量的类比，探讨非广延熵与强引力光学的关联。
摘要：
我们基于近视界光子气体模型，为Reissner--Nordström黑洞发展了一个非广延热力学框架，推导出广义Bekenstein--Hawking熵，其在广延极限下一致于Bekenstein--Hawking面积定律。诱导的变形导致热力学结构包含小、中等和大黑洞分支，表现出Van der Waals型相变特征。我们进一步通过将光子球观测到的轨道周期和李雅普诺夫指数与热力学变量关联，建立光学-热力学类比。这些光学特征在热力学临界行为和相结构上具有定性跟踪作用，暗示其在未来高分辨率测量中的潜在观测价值。这些结果可能为非广延熵、黑洞临界现象与强引力光学之间的概念联系提供启示。
英文摘要：
We develop a non-extensive thermodynamic framework for Reissner--Nordström black holes based on a near-horizon photon-gas model within Tsallis statistics. We derive the generalized Bekenstein--Hawking entropy based on such an approach, consistent with the Bekenstein--Hawking area law in the extensive limit, $q \rightarrow 1$. The induced deformation gives rise to a rich thermodynamic structure consisting of small, intermediate, and large black-hole branches, exhibiting Van der Waals-like phase transitions characterized by mean-field critical exponents. We further establish an optical--thermodynamic analogy by relating photon-sphere observables, including orbital periods and Lyapunov exponents, to thermodynamic variables. These optical signatures qualitatively track the thermodynamic critical behavior and phase structure, suggesting their potential relevance as observational probes in future high-resolution measurements. These results may shed light on a conceptual connection between non-extensive entropy, black-hole critical phenomena, and strong-gravity optics.
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