静态球对称空心核心的边界阻碍与 lapse 自由
Boundary Obstructions and Lapse Freedom in Static Spherical Hollow Cores
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中文总结 AI 辅助
本文研究静态球对称空心核心的边界阻碍问题，分析其能量条件违反情况，构建单位 lapse 下的正则空心壳族，得出静态边界定理与构造。
中文摘要 AI 辅助
我们针对静态球对称空心核心这一界限清晰的对比问题展开分析：该核心为一个空的平直空腔，外围被正物质壁包围。在单位 lapse（ lapse 指时移函数，此处为特定取值）、平直切片径向 Painleve–Gullstrand（PG）类中，I 型源满足 $p_r=-\rho$ 且 $p_\perp=-\rho-r\rho'/2$。因此，从空腔向外升高的正则非负密度必然违反横向零能量条件（NEC）和弱能量条件（WEC）。我们通过精确的加权 onset 预算以及深度-宽度界来量化这种边界阻碍，并证明该尖锐极限具有与其对称不变正则化 Israel 层相同的负切向压力。随后，在单调面积半径假设下，我们闭合相邻的单位 lapse、弯曲切片路径。最后，当仅释放 lapse 时，不完全 β 族给出正则空心壳，其具有平直空腔、史瓦西外区、无薄壳，且在明确的紧致区间上满足 NEC、WEC、SEC、DEC。该族在最小阶数和 $p_r=0$ 扇区中被条件性表征，并允许固定 ADM 质量的空腔红移基准。该结果是一个静态边界定理与构造，而非通用的空心壳存在定理、传输结果或实验可行性主张。
英文摘要
We analyze a sharply delimited comparison problem for a static spherical hollow core: an empty, flat cavity surrounded by a positive matter wall. In the unit-lapse, flat-slice radial Painleve--Gullstrand (PG) class the Type-I source obeys $p_r=-ρ$ and $p_\perp=-ρ-rρ'/2$. A regular nonnegative density that rises out of the cavity must therefore violate the transverse null and weak energy conditions. We quantify this boundary obstruction by an exact weighted onset budget and a depth--width bound, and show that the sharp limit has the same negative tangential pressure as its symmetry-invariant regularized Israel layer. We then close the adjacent unit-lapse, curved-slice route under a monotone areal-radius hypothesis. Finally, when only the lapse is released, an incomplete-beta family gives regular hollow shells with flat cavities, Schwarzschild exteriors, no thin shells, and NEC/WEC/SEC/DEC on an explicit compactness interval. The family is conditionally characterized in the minimum-degree and $p_r=0$ sectors and admits a fixed-ADM-mass cavity redshift benchmark. The result is a static boundary theorem and construction, not a general hollow-shell existence theorem, a transport result, or an experimental feasibility claim.
