## Weak null singularities in general relativity

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Jonathan Luk
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## Abstract:

We construct a class of spacetimes (without symmetry assumptions) satisfying the vacuum Einstein equations with singular boundaries on two null hypersurfaces intersecting in the future on a 2-sphere. The metric of these spacetimes extends continuously beyond the singularities while the Christoffel symbols fail to be square integrable in a neighborhood of any point on the singular boundaries. The construction shows moreover that the singularities are stable in a suitable sense. These singularities are stronger than the impulsive gravitational spacetimes considered by Luk and Rodnianski, and conjecturally they are present in the interior of generic black holes arising from gravitational collapse.## References

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## Additional Information

**Jonathan Luk**- Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305-2125
- MR Author ID: 916843
- Email: jluk@stanford.edu
- Received by editor(s): February 23, 2014
- Received by editor(s) in revised form: May 27, 2015
- Published electronically: September 27, 2017
- Additional Notes: This work is supported by the NSF Postdoctoral Fellowship DMS-1204493 and the NSF grant DMS-1709458.
- © Copyright 2017 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**31**(2018), 1-63 - MSC (2010): Primary 83C75, 35L67
- DOI: https://doi.org/10.1090/jams/888
- MathSciNet review: 3718450