最小长度尺度如何修改RN AdS黑洞的热力学？
How a minimal length scale modifies thermodynamics of RN AdS Black Holes?
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中文总结 AI 辅助
研究最小长度尺度对RN AdS黑洞热力学的影响，通过相空间对易关系构建修改后的度规来推导相关热力学量，分析热稳定性和P-V临界性等，发现最小长度尺度使共存区域和反转曲线变形，为量子引力提供观测特征。
中文摘要 AI 辅助
我们研究了由最小长度尺度引起的Reissner-Nordstroem反德西特（RN AdS）黑洞的热力学修改，该尺度自然出现在κ变形时空中。通过相空间对易关系构建修改后的度规，我们推导出变形的霍金温度、熵和焓。通过热容量分析热稳定性并研究P-V临界性，发现黑洞经历类似于范德瓦尔斯系统的从小到大规模的相变，尽管临界比因非对易性而略有降低。此外，我们研究了焦耳-汤姆逊膨胀，发现非对易（NC）参数在温度-压力平面上扩展了冷却区域。我们的结果表明，虽然与范德瓦尔斯流体的整体热力学类比仍然存在，但最小长度尺度系统地使共存区域和反转曲线变形，为量子引力提供了潜在的观测特征。
英文摘要
We investigate the thermodynamic modifications of the Reissner-Nordstroem anti-de Sitter (RN AdS) black hole induced by a minimal length scale,which naturally emerges in $κ$-deformed space-time. By constructing the modified metric via phase-space commutation relations,we derive the deformed Hawking temperature, entropy, and enthalpy. We analyze the thermal stability through the heat capacity and study the P-V criticality, revealing that the black hole undergoes a small-to-large phase transition analogous to the Van der Waals system, albeit with a critical ratio slightly lowered by non-commutativity. Furthermore, we examine the Joule-Thomson expansion and find that the non-commutative (NC) parameter expands the cooling region in the temperature-pressure plane. Our results demonstrate that while the overall thermodynamic analogy with the Van der Waals fluid persists, the minimal length scale systematically deform the coexistence region and inversion curves, offering potential observational signatures for quantum gravity.
