Asymptotic behavior in polarized T2-symmetric vacuum space–times

DOI10.1063/1.532775zbMath1061.83512arXiv1709.09715OpenAlexW1681051474MaRDI QIDQ4701718

Satyanad Kichenassamy, James A. Isenberg

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.09715

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Asymptotic procedures (radiation, news functions, (mathcal{H} )-spaces, etc.) in general relativity and gravitational theory (83C30)

Related Items (23)

On the nature of Hawking's incompleteness for the Einstein-vacuum equations: the regime of moderately spatially anisotropic initial data ⋮ Stable big bang formation in near-FLRW solutions to the Einstein-scalar field and Einstein-stiff fluid systems ⋮ The maximal development of near-FLRW data for the Einstein-scalar field system with spatial topology \(\mathbb{S}^3\) ⋮ Stability of AVTD behavior Within the polarized \(\mathbb{T}^2\)-symmetric vacuum spacetimes ⋮ Quasilinear hyperbolic Fuchsian systems and AVTD behavior in \(T ^{2}\)-symmetric vacuum spacetimes ⋮ A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges ⋮ Stable Big Bang formation for Einstein’s equations: The complete sub-critical regime ⋮ A regime of linear stability for the Einstein-scalar field system with applications to nonlinear Big Bang formation ⋮ Asymptotically Kasner-like singularities ⋮ Localized big bang stability for the Einstein-scalar field equations ⋮ Mathematical aspects of general relativity. Abstracts from the workshop held August 29 -- September 4, 2021 (hybrid meeting) ⋮ Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor ⋮ Areal foliation and asymptotically velocity-term dominated behavior in T2 symmetric space-times with positive cosmological constant ⋮ The Fuchsian approach to global existence for hyperbolic equations ⋮ A new class of asymptotically non-chaotic vacuum singularities ⋮ Instability of spatially homogeneous solutions in the class of \(\mathbb T^2\)-symmetric solutions to Einstein's vacuum equations ⋮ Numerical approaches to spacetime singularities ⋮ Theorems on existence and global dynamics for the Einstein equations ⋮ The Einstein-Vlasov system/kinetic theory ⋮ Local and global existence theorems for the Einstein equations ⋮ Theorems on existence and global dynamics for the Einstein equations ⋮ Contracting asymptotics of the linearized lapse-scalar field sub-system of the Einstein-scalar field equations ⋮ A Fuchsian viewpoint on the weak null condition

Cites Work

• Asymptotic behaviour of the gravitational field and the nature of singularities in Gowdy spacetimes
• On space-times with U(1)\(\times U(1)\) symmetric compact Cauchy surfaces
• Vacuum spacetimes with two-parameter spacelike isometry groups and compact invariant hypersurfaces: Topologies and boundary conditions
• Global foliations of vacuum spacetimes with \(T^2\) isometry
• Existence of constant mean curvature foliations in spacetimes with two-dimensional local symmetry
• Fuchsian equations in Sobolev spaces and blow-up
• Strong cosmic censorship in polarised Gowdy spacetimes
• Global dynamics of the mixmaster model
• A dynamical systems approach to Bianchi cosmologies: orthogonal models of class A
• The structure of WTC expansions and applications
• The blow-up problem for exponential nonlinearities
• Analytic description of singularities in Gowdy spacetimes

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