Areal Foliation and AVTD Behavior in T^2 Symmetric Spacetimes with Positive Cosmological Constant

Abstract

We prove a global foliation result, using areal time, for T^2 symmetric spacetimes with a positive cosmological constant. We then find a class of solutions that exhibit AVTD behavior near the singularity.

arXiv comment15 pages, 0 figures, 2 references added

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Cited by in corpus (12)

• Proof of the cosmic no-hair conjecture in the T^3-Gowdy symmetric Einstein-Vlasov setting
• Asymptotics and singularities in cosmological models with positive cosmological constant
• A New Class of Asymptotically Non-Chaotic Vacuum Singularities
• Non-genericity of the Nariai solutions: II. Investigations within the Gowdy class
• Localized big bang stability for the Einstein-scalar field equations
• On the initial geometry of a vacuum cosmological spacetime
• On the area of the symmetry orbits of cosmological spacetimes with toroidal or hyperbolic symmetry
• The annoying null boundaries
• Stability of AVTD Behavior within the Polarized $T^2$-symmetric vacuum spacetimes
• Stability of Asymptotic Behavior Within Polarised $T^2$-Symmetric Vacuum Solutions with Cosmological Constant
• On the Cosmic No-Hair Conjecture in T2-symmetric non-linear scalar field spacetimes
• Polarized Electrogowdy spacetimes censored