AI 中文总结
该研究在经典广义相对论中，将Λ-FLRW宇宙学里尖锐薄壳的暗晕初始数据嵌入改进为光滑正密度形式，满足约束与能量条件，残差随分辨率收敛，外部用解析FLRW解定义。
AI 中文摘要
在经典广义相对论框架内，我们对比了均匀Λ-FLRW环境中，正过剩维里化暗晕的类时尖锐接合与有限宽度类空光滑初始数据嵌入两种情况。在普通分支上，维里边界处的类时Israel匹配会产生负表面层，这是尖锐构造所省略的环境补偿的分布表示。我们将这个零宽度源替换为有限宽度、相对于背景的低密度区，其局部静止系能量密度保持为正。由此得到的共形平坦、常平均曲率ADM初始切片满足哈密顿量和动量约束，且残差随分辨率细化而收敛。在有限半径处，其几何和物质变量在规定容差内回到局域有效FLRW数据：所构造的切片不含剩余分布层，且满足重构的弱、零和主导能量条件。对于数值端点之外的半径，外部由精确解析的局域有效FLRW解定义。GCT框架提供全局动机时钟解释，而当前计算是局域有效经典广义相对论计算，其中边界区常数c0和G0保持固定：未构造径向GCT时移或常数插值。
英文摘要
Within classical general relativity, we compare a sharp timelike junction and a smooth finite-width spacelike initial-data embedding of a positive-excess virialized halo in a homogeneous Lambda-FLRW environment. On the ordinary branch, timelike Israel matching at the virial boundary produces a negative surface layer: a distributional representation of the environmental compensation omitted by the sharp construction. We replace this zero-width source by a finite-width, background-relative underdensity whose local rest-frame energy density remains positive. The resulting conformally flat, constant-mean-curvature ADM initial slice satisfies the Hamiltonian and momentum constraints, with the residuals converging under resolution refinement. At finite radius, its geometric and matter variables return to the local-effective FLRW data within the declared tolerances: the constructed slice contains no residual distributional layer and satisfies the reconstructed weak, null, and dominant energy conditions. For radii beyond the numerical endpoint, the exterior is defined by the exact analytic local-effective FLRW solution. The GCT framework supplies the global motivation clock interpretation, while the present calculations are local-effective classical-GR calculations with the bound-sector constants c0 and G0 held fixed: no radial GCT lapse or constant interpolation is constructed.
Comments31 pages, 6 figures
