AI 中文总结
该研究针对暗能量背景下坍缩尘埃的引力坍缩奇点问题，提出径向变化的尘埃-暗能量相互作用机制，构建出满足能量条件的正则黑洞模型，为传统正则黑洞模型提供了物理起源明确的替代方案。
AI 中文摘要
引力坍缩中的中心奇点代表经典广义相对论的根本性失效，但其解决仍是开放性挑战。传统正则黑洞模型引入奇异物质或非线性电动力学，而此类正则化机制的物理起源仍不明确。本工作证明，尘埃与暗能量之间的径向变化相互作用可自然解决中心奇点。我们系统研究三种情况：无相互作用、常数相互作用、径向变化相互作用。仅当相互作用向中心充分增长时，才能同时消除中心附近密度和中心质量贡献的发散行为，产生质量函数标度为 $M \sim \chi^3$、有限Kretschmann标量（$\lim_{\chi \to 0} K < \infty$），以及在物态方程 $w \leq -1$（$w=-1$对应纯德西特核心）下的类德西特核心。在中心，所得构型满足零能量条件、弱能量条件和主能量条件，而强能量条件被违反。与基于电荷的模型不同，我们的相互作用参数 $\alpha(t)$ 在坍缩后稳定为非零值，使正则核心能在后期构型中持续存在。这为传统正则黑洞模型提供了物理动机明确的替代方案，其基础是现代暗能量的宇宙学理解，而非奇异场或电荷。
英文摘要
The central singularity in gravitational collapse represents a fundamental breakdown of classical general relativity, yet its resolution remains an open challenge. While conventional regular black hole models invoke exotic matter or nonlinear electrodynamics, the physical origin of such regularization mechanisms remains obscure. In this work, we demonstrate that a radially varying interaction between dust and dark energy can naturally resolve the central singularity. We systematically investigate three cases: no interaction, constant interaction, and radially varying interaction. Only when the interaction grows sufficiently toward the center can the divergent behavior of the density and the central mass contribution simultaneously be eliminated near the center. This yields a mass function scales as $M \sim χ^3$, a finite Kretschmann scalar ($\lim_{χ\to 0} K < \infty$), and a de Sitter-like core for the physical regime $w \leq -1$ (with $w=-1$ corresponding to pure de Sitter core). At the center, the resulting configuration satisfies the null, weak, and dominant energy conditions, while the strong energy condition is violated. Unlike charge-based models, our interaction parameter $α(t)$ stabilizes at a non-zero value after the collapse, allowing the regular core to persist in the late-time configuration. This provides a physically motivated alternative to conventional regular black hole models, grounded in the modern cosmological understanding of dark energy rather than exotic fields or charges.
