High-frequency backreaction for the Einstein equations under polarized \(\mathbb U(1)\)-symmetry

DOI10.1215/00127094-2018-0035zbMath1412.35327arXiv1706.09501OpenAlexW3105835409WikidataQ128935187 ScholiaQ128935187MaRDI QIDQ1712810

Jonathan Luk, Cécile Huneau

Publication date: 31 January 2019

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.09501

zbMATH Keywords

general relativity

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) PDEs in connection with relativity and gravitational theory (35Q75) Einstein equations (35Q76)

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Cites Work

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• Concentration compactness for critical wave maps
• The bounded \(L^2\) curvature conjecture
• Regularity of wave-maps in dimension \(2+1\)
• Global regularity for the 2+1 dimensional equivariant Einstein-wave map system
• Stability of Minkowski space-time with a translation space-like Killing field
• Einstein equations under polarized \(\mathbb{U}(1)\) symmetry in an elliptic gauge
• Nonlinear interaction of impulsive gravitational waves for the vacuum Einstein equations
• A proof of the instability of AdS for the Einstein-null dust system with an inner mirror
• Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data II: the exterior of the Black Hole region
• Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data. I: The interior of the black hole region
• Collapsing in the Einstein flow
• The high-frequency limit in general relativity
• The behavior of the laplacian on weighted sobolev spaces
• Backreaction in the future behavior of an expanding vacuum spacetime
• The interior of charged black holes and the problem of uniqueness in general relativity
• Some high-frequency spherical gravity waves
• Local Propagation of Impulsive GravitationalWaves
• No Black-Hole Theorem in Three-Dimensional Gravity
• Global regularity of wave maps. II: Small energy in two dimensions
• Constraint equations for \(3 + 1\) vacuum Einstein equations with a translational space-like Killing field in the asymptotically flat case

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