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 Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/30003

 Title: Breakdown Criteria for Nonvacuum Einstein Equations Authors: Shao, Arick Keywords: General RelativityEinstein EquationsNull conesBreakdown criteria Issue Date: 13-Oct-2011 Series/Report no.: Analysis and Applied Math Seminar2011-10-07 Abstract: We extend a recent breakdown/continuation result of S. Klainerman and I. Rodnianski for the Einstein-vacuum equations to the Einstein-scalar and the Einstein-Maxwell equations. Roughly, the main theorem states that if an existing local solution of these equations satisfy certain uniform bounds for the second fundamental form, lapse, and matter field, then it can be further extended in time. This can also be reformulated as conditions that must be satisfied when such a solution blows up. In particular, in these nonvacuum settings, we encounter additional difficulties resulting from the nontrivial Ricci curvature and from the coupling between the Einstein and the matter field equations. URI: http://hdl.handle.net/1807/30003 Appears in Collections: Department of Mathematics

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