AI 中文总结
本文研究被理想流体暗物质包围的两类黑洞的热力学性质与信息恢复，揭示暗物质会改变霍金温度、加速蒸发与信息恢复，且通过岛公式重现佩奇曲线恢复信息守恒。
AI 中文摘要
本文研究被理想流体暗物质包围的史瓦西（Schwarzschild）黑洞和雷斯纳-诺德斯特龙（Reissner--Nordström）黑洞的热力学性质与信息恢复。研究表明，尽管贝肯斯坦-霍金（Bekenstein--Hawking）熵保持不变，但暗物质通过引入正贡献显著改变霍金温度，增强了热效应，尤其对小黑洞更为明显。研究发现相结构得以保留：史瓦西黑洞仍保持不稳定，而雷斯纳-诺德斯特龙黑洞呈现标准的小/大黑洞相变，其中小黑洞稳定、大黑洞不稳定。此外，研究证实暗物质会加速霍金蒸发，从而缩短黑洞寿命。进一步利用岛公式（island formula）研究黑洞信息丢失悖论：无岛时，霍金辐射的纠缠熵随时间线性增长，后期发散，违反幺正性；引入岛贡献后，霍金辐射的纠缠熵饱和于两倍的贝肯斯坦-霍金熵，重现佩奇曲线（Page curve），恢复了被理想流体暗物质包围的史瓦西和雷斯纳-诺德斯特龙黑洞的信息恢复能力。研究推导了佩奇时间（Page time）的解析表达式，证明其直接由黑洞的热力学参数决定；还建立了热力学与信息恢复的对应关系，表明佩奇时间受霍金温度和事件视界支配；最终发现暗物质的存在会缩短佩奇时间，从而加速信息恢复。
英文摘要
In this paper, we investigate the thermodynamic properties and information recovery of Schwarzschild and Reissner--Nordstr"om black holes surrounded by perfect fluid dark matter. We show that, while the Bekenstein--Hawking entropy remains unchanged, dark matter significantly modifies the Hawking temperature by introducing a positive contribution that enhances thermal effects, particularly for small black holes. We find that the phase structure is preserved: Schwarzschild black holes remain unstable, whereas Reissner--Nordstr"om black holes exhibit the standard small/large black hole transition, in which small black holes are stable and large black holes are unstable. Furthermore, we demonstrate that dark matter accelerates Hawking evaporation, thereby reducing black hole lifetimes. We further investigate the black hole information loss paradox using the island formula. In the absence of islands, the entanglement entropy of Hawking radiation grows linearly with time and diverges at late times, thereby violating unitarity. By including island contributions, the entanglement entropy of Hawking radiation saturates at twice the Bekenstein--Hawking entropy, reproducing the Page curve and restoring information recovery for both Schwarzschild and Reissner--Nordstr"om black holes surrounded by perfect fluid dark matter. We derive analytical expressions for the Page time and demonstrate that it is directly determined by the thermodynamic parameters of the black hole. Furthermore, we establish a correspondence between thermodynamics and information recovery by showing that the Page time is governed by the Hawking temperature and the event horizon. Finally, we find that the presence of dark matter reduces the Page time, thereby accelerating information recovery.
Comments20 pages, 1O figures. arXiv:submit/7905627 [gr-qc]
