TY - JOUR
T1 - Naked singularities for the Einstein vacuum equations
T2 - The exterior solution
AU - Rodnianski, Igor
AU - Shlapentokh-Rothman, Yakov
N1 - 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
SN - 0003-486X
VL - 198
SP - 231
EP - 391
JO - Annals of Mathematics
JF - Annals of Mathematics
IS - 1
ER -