Stability of AVTD Behavior Within the Polarized T2 -Symmetric Vacuum Spacetimes

Ellery Ames; Florian Beyer; James Isenberg; Todd A. Oliynyk

doi:10.1007/s00023-021-01142-0

Stability of AVTD Behavior Within the Polarized T² -Symmetric Vacuum Spacetimes

Ellery Ames, Florian Beyer, James Isenberg, Todd A. Oliynyk

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

We prove stability of the family of Kasner solutions within the class of polarized T²-symmetric solutions of the vacuum Einstein equations in the contracting time direction with respect to an areal time foliation. All Kasner solutions for which the asymptotic velocity parameter K satisfies | K- 1 | > 2 are non-linearly stable, and all sufficiently small perturbations exhibit asymptotically velocity term dominated (AVTD) behavior and blow-up of the Kretschmann scalar.

Original language	English
Pages (from-to)	2299–2343
Number of pages	45
Journal	Annales Henri Poincare
Volume	23
Issue number	7
DOIs	https://doi.org/10.1007/s00023-021-01142-0
Publication status	Published - 23 Jan 2022

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10.1007/s00023-021-01142-0

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title = "Stability of AVTD Behavior Within the Polarized T2 -Symmetric Vacuum Spacetimes",

abstract = "We prove stability of the family of Kasner solutions within the class of polarized T2-symmetric solutions of the vacuum Einstein equations in the contracting time direction with respect to an areal time foliation. All Kasner solutions for which the asymptotic velocity parameter K satisfies | K- 1 | > 2 are non-linearly stable, and all sufficiently small perturbations exhibit asymptotically velocity term dominated (AVTD) behavior and blow-up of the Kretschmann scalar.",

author = "Ellery Ames and Florian Beyer and James Isenberg and Oliynyk, {Todd A.}",

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AU - Oliynyk, Todd A.

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Y1 - 2022/1/23

N2 - We prove stability of the family of Kasner solutions within the class of polarized T2-symmetric solutions of the vacuum Einstein equations in the contracting time direction with respect to an areal time foliation. All Kasner solutions for which the asymptotic velocity parameter K satisfies | K- 1 | > 2 are non-linearly stable, and all sufficiently small perturbations exhibit asymptotically velocity term dominated (AVTD) behavior and blow-up of the Kretschmann scalar.

AB - We prove stability of the family of Kasner solutions within the class of polarized T2-symmetric solutions of the vacuum Einstein equations in the contracting time direction with respect to an areal time foliation. All Kasner solutions for which the asymptotic velocity parameter K satisfies | K- 1 | > 2 are non-linearly stable, and all sufficiently small perturbations exhibit asymptotically velocity term dominated (AVTD) behavior and blow-up of the Kretschmann scalar.

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Stability of AVTD Behavior Within the Polarized T2 -Symmetric Vacuum Spacetimes

Abstract

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Stability of AVTD Behavior Within the Polarized T² -Symmetric Vacuum Spacetimes