## On the breakdown criterion in general relativity

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- by Sergiu Klainerman and Igor Rodnianski
- J. Amer. Math. Soc.
**23**(2010), 345-382 - DOI: https://doi.org/10.1090/S0894-0347-09-00655-9
- Published electronically: December 24, 2009
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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.## References

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## Bibliographic Information

**Sergiu Klainerman**- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
- MR Author ID: 102350
- Email: seri@math.princeton.edu
**Igor Rodnianski**- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
- Email: irod@math.princeton.edu
- 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 - © Copyright 2009 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**23**(2010), 345-382 - MSC (2010): Primary 35J10
- DOI: https://doi.org/10.1090/S0894-0347-09-00655-9
- MathSciNet review: 2601037