TY - JOUR

T1 - Naked singularities for the Einstein vacuum equations

T2 - The exterior solution

AU - Rodnianski, Igor

AU - Shlapentokh-Rothman, Yakov

N1 - Funding Information:
1.5. Acknowledgements. The authors would like to thank Mihalis Dafer-mos for valuable discussions and comments on the manuscript. IR is partially supported by the NSF grant DMS-1709270 and a Simons Investigator Award. YS acknowledges support from NSF grant DMS-1900288, from an Alfred P. Sloan Fellowship in Mathematics, and from NSERC discovery grants RGPIN-2021-02562 and DGECR-2021-00093.
Publisher Copyright:
© 2023 Department of Mathematics, Princeton University.

PY - 2023

Y1 - 2023

N2 - In this work we initiate the mathematical study of naked singularities for the Einstein vacuum equations in 3 + 1 dimensions by constructing solutions which correspond to the exterior region of a naked singularity. A key element is our introduction of a new type of self-similarity for the Einstein vacuum equations. Connected to this is a new geometric twisting phenomenon which plays the leading role in singularity formation. Prior to this work, the only known examples of naked singularities were the solutions constructed by Christodoulou for the spherically symmetric Einstein-scalar-field system, as well as other solutions explored numerically for either the spherically symmetric Einstein equations coupled to suitable matter models or for the Einstein equations in higher dimensions.

AB - In this work we initiate the mathematical study of naked singularities for the Einstein vacuum equations in 3 + 1 dimensions by constructing solutions which correspond to the exterior region of a naked singularity. A key element is our introduction of a new type of self-similarity for the Einstein vacuum equations. Connected to this is a new geometric twisting phenomenon which plays the leading role in singularity formation. Prior to this work, the only known examples of naked singularities were the solutions constructed by Christodoulou for the spherically symmetric Einstein-scalar-field system, as well as other solutions explored numerically for either the spherically symmetric Einstein equations coupled to suitable matter models or for the Einstein equations in higher dimensions.

KW - naked singularity

KW - singularity

KW - weak cosmic censorship

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U2 - 10.4007/ANNALS.2023.198.1.3

DO - 10.4007/ANNALS.2023.198.1.3

M3 - Article

AN - SCOPUS:85163298098

SN - 0003-486X

VL - 198

SP - 231

EP - 391

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 1

ER -