[论文解读] Reissner Nordstrom black holes with integrable singularity interiors supported by string distributions

Milko Estrada|arXiv (Cornell University)|Feb 3, 2026

Black Holes and Theoretical Physics被引用 0

一句话总结

论文提出带弦云与新型弦流体的黑洞内部结构，具有可积奇点，外部匹配 Reissner–Nordström 时空并推导触界条件，实现温度连续性并可能存在相变。

ABSTRACT

The Reissner Nordstrom (RN) black hole is characterized by two well known pathologies: a central singularity and an inner horizon associated with instabilities and a potential loss of predictability. In this work, we show that the RN exterior geometry can arise from an interior spacetime containing an integrable singularity but no inner horizon. In this scenario, tidal forces remain finite near the origin, allowing nondestructive radial infall, while the conventional description in terms of a pointlike mass is replaced by an extended matter distribution. To illustrate this possibility, we provide explicit realizations of such an interior region based on string distributions, namely a cloud of strings (CS) and a newly defined fluid of strings (FS). While the standard cloud of strings model leads to a divergence in the conserved energy associated with timelike Killing vectors, the proposed FS model can be interpreted as a geometrically screened version of the string cloud distribution and admits configurations that, when extended to infinity, describe black holes with finite conserved energy. Physical consistency between the interior region and the RN exterior geometry requires the continuity of temperature across the interface, implying thermal equilibrium between the two regions, while discontinuities in the tangential pressure can signal gravitational phase transitions. These results determine the physical conditions under which string based interior distributions can consistently generate the RN exterior geometry and clarify the circumstances under which phase transitions at the event horizon may arise.

研究动机与目标

• 激励并构建具有可积奇点的内部几何以避免不稳定的内部视界与类宇宙常数核心；
• 通过几何屏蔽将云状弦能密度转化为有限能量的弦流体内部结构；
• 推导内部与外部区域的接界条件并分析热力学连续性及潜在的相变；
• 以两种显式的基于RN的外部情形作为测试配置（弦云内部与RN外部；新型弦流体内部与RN外部）。

提出的方法

• 对弦流体给出状态方程：ρ(fs)=α(r) p(fs)并推导内部度规函f(r)；
• 提出屏蔽的弦密度轮廓ρ(fs)=M/(4π b^2 r^2) exp(−r/b)以确保守恒能量M有限；
• 对静态、球对称内部求解爱因斯坦方程，获得在r=0处具有可积奇点的f(r)；
• 在视界处施加Israel–Darmois接界条件，确保一阶与二阶基本形式的连续性并分析温度连续性；
• 计算内部与外部张力与温度，将相变与切向压力的不连续性联系起来；
• 将该框架应用到两个RN基测试几何： (i) 内部弦云与RN外部； (ii) 内部弦流体与RN外部。

实验结果

研究问题

• RQ1 在何种内部物质分布下可实现黑洞内部的可积奇点，同时避免内部视界？
• RQ2 在事件视界处连接任意内部IS与外部RN几何的精确接界条件是什么？
• RQ3 内部–外部的匹配是否强制温度连续，切向压力的不连续性如何与相变相关？
• RQ4 弦云或新型弦流体内部结构是否能在RN条件下与Schwarzschild状的外部相匹配？

主要发现

• 一个新的弦流体黑洞解显示出带可积奇点且无内部视界；
• 几何屏蔽云状弦能密度可产生有限的守恒能量M；
• 内部解使f(r)从负值的极小点上升到视界，在r→0附近实现可积的动力学；
• Israel–Darmois接界条件意味着视界处度量及径向压力连续，并强制在视界处f的一阶导数连续，进而与温度概念相关；
• 对于具有云状弦的RN外部的内部匹配，特定的匹配条件关联参数a与l并产生有限的内部宇宙常数；
• 第二个示例（新型弦流体内部）给出明确的f(r)=1 − (2M/r)(1 − e^(−r/b)) + r^2/l^2，并具有类似的接界条件结构。