On the geometry of null cones in Einstein-vacuum spacetimes
Qian Wang
Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, USA
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Abstract
In this paper we study the geometry of null cones in smooth Einstein vacuum spacetimes. We provide the estimate for the trace of the null second fundamental form, as well as estimates for other geometric quantities. This paper is based on the work of Klainerman and Rodnianski [S. Klainerman, I. Rodnianski, Causal geometry of Einstein-vacuum spacetimes with finite curvature flux, Invent. Math. 159 (3) (2005) 437–529; S. Klainerman, I. Rodnianski, Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux, Geom. Funct. Anal. 16 (1) (2006) 164–229; S. Klainerman, I. Rodnianski, A geometric Littlewood–Paley theory, Geom. Funct. Anal. 16 (1) (2006) 126–163].
Cite this article
Qian Wang, On the geometry of null cones in Einstein-vacuum spacetimes. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 1, pp. 285–328
DOI 10.1016/J.ANIHPC.2008.03.002