博恩几何、元粒子与模黑洞残余的有效几何实现：史瓦西奇点的相空间分辨率
Born Geometry, Metaparticles, and an Effective Geometric Realization of the Modular Black-Hole Remnant: A Phase-Space Resolution of the Schwarzschild Singularity
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中文总结 AI 辅助
本研究在博恩几何等框架内构建了模黑洞残余的有效几何实现，规避了霍金-彭罗斯奇点定理的聚焦假设，揭示史瓦西奇点被有限博恩几何相空间结构取代。
中文摘要 AI 辅助
近期关于元粒子黑洞热力学的研究表明，存在一个有限的蒸发终点，其特征为最小视界面积、最大霍金温度以及稳定的冷模残余，但对应的时空几何仍未知。本研究在博恩几何、模时空和元粒子动力学框架内构建了模残余的有效几何实现。从补充了对偶坐标的双相空间描述出发，我们推导了由博恩不变径向距离支配的博恩加倍史瓦西几何。相关的模不确定关系禁止在相空间原点任意定位，使经典史瓦西奇点在物理上不可达，取而代之的是有限的模核心。随后我们纳入元粒子对偶约束，该约束会诱导博恩几何背景的有效共形形变，并产生非平凡的有效应力-能量张量。由此产生的内部区域形成了以张力主导的径向 sector 为特征的有限各向异性源。在模核心附近自然出现径向零能量条件和强能量条件的局域违反，提供了一种规避霍金-彭罗斯奇点定理所基于的聚焦假设的机制。这些结果确立了从元粒子黑洞热力学推断出的模残余的有效几何对应物，并表明史瓦西奇点被有限的博恩几何相空间结构取代，其紫外行为由对偶的非几何自由度支配。
英文摘要
Recent work on metaparticle black-hole thermodynamics suggested the existence of a finite evaporation endpoint characterized by a minimal horizon area, a maximal Hawking temperature, and a stable cold modular remnant. However, the corresponding spacetime geometry remained unknown. In this work we construct an effective geometric realization of the modular remnant within the framework of Born geometry, modular spacetime, and metaparticle dynamics. Starting from a doubled phase-space description in which spacetime coordinates are supplemented by dual coordinates, we derive a Born-doubled Schwarzschild geometry governed by a Born-invariant radial distance. The associated modular uncertainty relation prevents arbitrary localization at the phase-space origin, rendering the classical Schwarzschild singularity physically inaccessible and replacing it with a finite modular core. We then incorporate the metaparticle duality constraint, which induces an effective conformal deformation of the Born-geometric background and generates a nontrivial effective stress-energy tensor. The resulting interior region develops a finite anisotropic source characterized by a tension-dominated radial sector. Localized violations of the radial Null Energy Condition and the Strong Energy Condition arise naturally near the modular core, providing a mechanism through which the focusing assumptions underlying the Hawking--Penrose singularity theorems are evaded. These results establish an effective geometric counterpart of the modular remnant inferred from metaparticle black-hole thermodynamics and suggest that the Schwarzschild singularity is replaced by a finite Born-geometric phase-space structure whose ultraviolet behavior is governed by dual, non-geometric degrees of freedom.
