AI 中文总结
研究弯曲类空奇点处连续洛伦兹延拓的局部障碍，通过特定条件和几何步骤构建相关时空并分类测地线端点，得出单视界伯明翰 - 科特勒族在特定条件下\(C^0\)不可延拓的结论。
AI 中文摘要
我们在一类弯曲类空奇点处建立了连续洛伦兹延拓的局部障碍。该准则通过两个可积条件、相对扭曲因子的单调性条件以及纵向因子的发散来表示；它不要求封闭纤维有任何对称性。主要几何步骤是对终端因果迹进行径向压缩，这取代了球对称中可用的旋转变形。压缩在适配的边界图中产生一个紧致的时间分隔器。纵向平移然后产生在本征上发散但在延拓图中保持均匀控制的径向切片距离。接下来，我们在全局克鲁斯卡尔坐标中构建规范的单视界伯明翰 - 科特勒时空，并对其类时测地线的所有有限固有时端点进行分类。由此，由假定延拓提供的每个接近边界的有限极大值都被迫趋向奇异端点。局部障碍和测地线分类意味着对于具有非正宇宙学常数且每个封闭连通纤维满足\(\text{Ric}_{\gamma_\Sigma}=(n - 2)k\gamma_\Sigma\)的单视界伯明翰 - 科特勒族，在没有均匀性、可定向性或简单连通性假设的情况下\(C^0\)不可延拓。
英文摘要
We establish a local obstruction to continuous Lorentzian extensions at a class of warped spacelike singularities. The criterion is expressed through two integrability conditions, a monotonicity condition on the relative warp factors, and divergence of the longitudinal factor; it does not require any symmetry of the closed fiber. The main geometric step is a radial compression of terminal causal traces, which replaces the rotational deformation available in spherical symmetry. The compression yields a compact chronological separator in an adapted boundary chart. Longitudinal translations then produce radial-slice distances that diverge intrinsically while remaining uniformly controlled in the extension chart. Next, we construct the canonical one-horizon Birmingham-Kottler spacetime in global Kruskal coordinates and classify all finite proper-time ends of its timelike geodesics. Every boundary-approaching finite maximizer supplied by a putative extension is thereby forced to the singular end. The local obstruction and the geodesic classification imply $C^0$-inextendibility for the one-horizon Birmingham-Kottler family with nonpositive cosmological constant and every closed connected fiber satisfying $\text{Ric}_{γ_Σ}=(n-2)kγ_Σ$, without assumptions of homogeneity, orientability, or simple connectivity.
Comments29 pages, no figure. Comments are welcome. During preparation of this paper, we become aware of K. Mosani Arxiv 2606.25755 which may have overlap results
