Achronal Limits, Lorentzian Spheres, and Splitting
Achronal Limits, Lorentzian Spheres, and Splitting
复制标题
非时间极限、洛伦兹球和分裂
DOI：
10.1007/s00023-013-0305-1
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
C. Vega
中科院分区：
文献类型：
--
作者：
G. Galloway;C. Vega
20 世纪 80 年代初，丘提出了建立霍金-彭罗斯奇点定理的刚性问题。解决这个问题的方法涉及洛伦兹布斯曼函数的引入以及对其水平集——星球层——的几何学的研究。洛伦兹情形中的正则性理论比黎曼情形中的正则性理论要复杂得多且不太完整。在本文中，我们介绍了洛伦兹几何中星球概念的广泛概括，并采用完全不同（且高度几何化）的正则性方法。这些广义星球层是根据非时间限制来定义的，而我们获得的改进的规律性是基于非时间边界的规律性特性。我们建立了广义星圈的分裂结果，当它专门用于柯西星圈时，会产生巴特尼克分裂猜想的新结果，这是丘提出的问题的具体实现。我们的方法也适用于具有正宇宙学常数的时空。我们获得了未来渐近德西特时空的刚性奇点结果，与 Andersson 和 Galloway (Adv Theor Math Phys 6:307–327, 2002) 以及 Cai 和 Galloway (Adv Theor Math Phys 3:1769–1783, 2000) 的结果相关。
In the early 1980s Yau posed the problem of establishing the rigidity of the Hawking–Penrose singularity theorems. Approaches to this problem have involved the introduction of Lorentzian Busemann functions and the study of the geometry of their level sets—the horospheres. The regularity theory in the Lorentzian case is considerably more complicated and less complete than in the Riemannian case. In this paper, we introduce a broad generalization of the notion of horosphere in Lorentzian geometry and take a completely different (and highly geometric) approach to regularity. These generalized horospheres are defined in terms of achronal limits, and the improved regularity we obtain is based on regularity properties of achronal boundaries. We establish a splitting result for generalized horospheres, which when specialized to Cauchy horospheres yields new results on the Bartnik splitting conjecture, a concrete realization of the problem posed by Yau. Our methods are also applied to spacetimes with positive cosmological constant. We obtain a rigid singularity result for future asymptotically de Sitter spacetimes related to results in Andersson and Galloway (Adv Theor Math Phys 6:307–327, 2002), and Cai and Galloway (Adv Theor Math Phys 3:1769–1783, 2000).
洛伦兹流形和奇点定理中超曲面的体积比较
影响因子：
0.7
作者：
J.-H. Treude;J.D.E. Grant
通讯作者：
J.D.E. Grant