发表机构
University of Hamburg; University of Toronto; University of Alberta; SISSA（汉堡大学; 多伦多大学; 阿尔伯塔大学; 国际高等研究学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文在类时截面曲率有下界且下界接近零的全局双曲时空中，证明了一个几乎分裂定理，表明长极大类时线段附近的因果钻石在洛伦兹Gromov--Hausdorff意义下接近乘积时空，为洛伦兹分裂定理提供了定量版本。
AI 中文摘要
我们建立了类时截面曲率界下时空的几乎分裂定理，其精神与Cheeger和Colding的著名黎曼结果一致。更具体地，我们证明：若一个全局双曲时空的类时截面曲率有下界，且该下界为接近零的非正常数，且该时空包含一条长的极大类时线段，则沿该线段的因果钻石在Minguzzi--Suhr的洛伦兹Gromov--Hausdorff意义下接近乘积度量时空中的因果钻石。我们的结果可视为Beem--Ehrlich--Markvorsen--Galloway关于非负类时截面曲率时空的洛伦兹分裂定理的定量类比。
英文摘要
We establish an almost-splitting theorem for spacetimes under timelike sectional curvature bounds in the spirit of the celebrated Riemannian result due to Cheeger and Colding. More concretely, we show that if a globally hyperbolic spacetime with timelike sectional curvature bounded below by a nonpositive constant close to zero contains a long maximizing timelike segment, then causal diamonds along that segment are close in the Lorentzian Gromov--Hausdorff sense of Minguzzi--Suhr to those in a product metric spacetime. Our result can be interpreted as a quantitative analogue of the Lorentzian splitting theorem for spacetimes with nonnegative timelike sectional curvature by Beem--Ehrlich--Markvorsen--Galloway.
Comments38 pages, comments welcome
