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On the breakdown criterion in general relativity


Authors: Sergiu Klainerman and Igor Rodnianski
Journal: J. Amer. Math. Soc. 23 (2010), 345-382
MSC (2010): Primary 35J10
DOI: https://doi.org/10.1090/S0894-0347-09-00655-9
Published electronically: December 24, 2009
MathSciNet review: 2601037
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Abstract: We give a geometric criterion for the breakdown of an Einstein-vacuum space-time foliated by a constant mean curvature, or maximal, foliation. More precisely we show that the foliated space-time can be extended as long as the second fundamental form and the first derivatives of the logarithm of the lapse of the foliation remain uniformly bounded. We make no restrictions on the size of the initial data. The paper uses heavily the results of the authors' previous papers.


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Additional Information

Sergiu Klainerman
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: seri@math.princeton.edu

Igor Rodnianski
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: irod@math.princeton.edu

DOI: https://doi.org/10.1090/S0894-0347-09-00655-9
Received by editor(s): February 4, 2008
Published electronically: December 24, 2009
Additional Notes: The first author is partially supported by NSF grant DMS-0070696
The second author is partially supported by NSF grant DMS-0702270
Article copyright: © Copyright 2009 American Mathematical Society