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Weak null singularities in general relativity


Author: Jonathan Luk
Journal: J. Amer. Math. Soc. 31 (2018), 1-63
MSC (2010): Primary 83C75, 35L67
DOI: https://doi.org/10.1090/jams/888
Published electronically: September 27, 2017
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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.


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Additional Information

Jonathan Luk
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305-2125
Email: jluk@stanford.edu

DOI: https://doi.org/10.1090/jams/888
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.
Article copyright: © Copyright 2017 American Mathematical Society

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