Stability of asymptotic behaviour within polarized T2-symmetric vacuum solutions with cosmological constant
Stability of asymptotic behaviour within polarized T2-symmetric vacuum solutions with cosmological constant
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DOI：
10.1098/rsta.2021.0173
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发表时间：
2021-08
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影响因子：
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通讯作者：
E. Ames;F. Beyer;J. Isenberg;T. Oliynyk
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文献类型：
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作者：
E. Ames;F. Beyer;J. Isenberg;T. Oliynyk
我们证明了在具有任意宇宙学常数 Λ 的真空爱因斯坦方程的极化 T2 对称解类中，Kasner 解子族的摄动在收缩时间方向上的渐近行为的非线性稳定性。该稳定性结果概括了 Ames E 等人证明的结果。 （2022 极化 T2 对称真空时空内 AVTD 行为的稳定性。Ann. Henri Poincaré。（doi:10.1007/s00023-021-01142-0）），重点关注 Λ=0 情况，正如该文章中一样，证明依赖于实时叶状结构和 Fuchsian 技术。即使对于 Λ=0，这里建立的结果也适用于极化 T2 对称真空解族中 Kasner 解的更广泛的扰动，而不是 Ames E 等人中考虑的结果。 （2022 偏振 T2 对称真空时空内 AVTD 行为的稳定性。Ann. Henri Poincaré。（doi：10.1007/s00023-021-01142-0））和 Fournodavlos G 等人。 （2020 年爱因斯坦方程的稳定大爆炸形成：完整的亚临界状态。预印本。(http://arxiv.org/abs/2012.05888)）。我们的结果表明，对于某些具有宇宙学常数的极化 T2 对称解族，对于某些 T0>0，区域时间坐标采用 (0,T0] 中的所有值。本文是主题问题“数学宇宙学的未来，第 1 卷”的一部分。
We prove the nonlinear stability of the asymptotic behaviour of perturbations of subfamilies of Kasner solutions in the contracting time direction within the class of polarized T2-symmetric solutions of the vacuum Einstein equations with arbitrary cosmological constant Λ. This stability result generalizes the results proven in Ames E et al. (2022 Stability of AVTD Behavior within the Polarized T2-symmetric vacuum spacetimes. Ann. Henri Poincaré. (doi:10.1007/s00023-021-01142-0)), which focus on the Λ=0 case, and as in that article, the proof relies on an areal time foliation and Fuchsian techniques. Even for Λ=0, the results established here apply to a wider class of perturbations of Kasner solutions within the family of polarized T2-symmetric vacuum solutions than those considered in Ames E et al. (2022 Stability of AVTD Behavior within the Polarized T2-symmetric vacuum spacetimes. Ann. Henri Poincaré. (doi:10.1007/s00023-021-01142-0)) and Fournodavlos G et al. (2020 Stable Big Bang formation for Einstein’s equations: the complete sub-critical regime. Preprint. (http://arxiv.org/abs/2012.05888)). Our results establish that the areal time coordinate takes all values in (0,T0] for some T0>0, for certain families of polarized T2-symmetric solutions with cosmological constant. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.