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July  2010, 28(3): 1007-1031. doi: 10.3934/dcds.2010.28.1007

On emerging scarred surfaces for the Einstein vacuum equations

Sergiu Klainerman 1, and  Igor Rodnianski 2,

1. 

Department of Mathematics, Princeton University, Princeton, NJ 08544,, United States
2. 

Department of Mathematics, Princeton University, Princeton, NJ 08544, United States

Received  March 2010 Revised  April 2010 Published  April 2010

We follow up our work [4] concerning the formation of trapped surfaces. We provide a considerable extension of our result there on pre-scared surfaces to allow for the formation of a surface with multiple pre-scared angular regions which, together, can cover an arbitrarily large portion of the surface. In a forthcoming paper we plan to show that once a significant part of the surface is pre-scared, it can be additionally deformed to produce a bona-fide trapped surface.
Keywords: Ricci coefficients, vacuum, characteristic., black hole, expansion, trapped surface, scarred surface, double null foliation, Einstein equations, null second fundamental form, energy estimates.
Mathematics Subject Classification: 35J1.
Citation: Sergiu Klainerman, Igor Rodnianski. On emerging scarred surfaces for the Einstein vacuum equations. Discrete & Continuous Dynamical Systems, 2010, 28 (3) : 1007-1031. doi: 10.3934/dcds.2010.28.1007
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