Causal geometry of Einstein-Vacuum spacetimes with finite curvature flux

• 成果类型: Article
• 署名作者: Klainerman, S; Rodnianski, I
• 署名单位: Princeton University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0365-4
• 发表日期: 2005
• 页码: 437-529
• 关键词: linear wave-equations; local existence; SINGULARITIES

摘要

One of the central difficulties of settling the L-2-bounded curvature conjecture for the Einstein-Vacuum equations is to be able to control the causal structure of spacetimes with such limited regularity. In this paper we show how to circumvent this difficulty by showing that the geometry of null hypersurfaces of Enstein-Vacuum spacetimes can be controlled in terms of initial data and the total curvature flux through the hypersurface.