On the area of the symmetry orbits in $T^2$ symmetric spacetimes

Abstract

We obtain a global existence result for the Einstein equations. We show that in the maximal Cauchy development of vacuum $T^2$ symmetric initial data with nonvanishing twist constant, except for the special case of flat Kasner initial data, the area of the $T^2$ group orbits takes on all positive values. This result shows that the areal time coordinate $R$ which covers these spacetimes runs from zero to infinity, with the singularity occurring at R=0.

arXiv commentThe appendix which appears in version 1 has a technical problem (the inequality appearing as the first stage of (52) is not necessarily true), and since the appendix is unnecessary for the proof of our results, we leave it out. version 2 -- clarifications added, version 3 -- reference corrected

References in corpus (5)

• Global Foliations of Vacuum Spacetimes with $T^2$ Isometry
• Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on $T^3\times R$
• Global foliations of matter spacetimes with Gowdy symmetry
• Oscillatory approach to the singularity in vacuum spacetimes with $T^2$ isometry
• Exact U(1) symmetric cosmologies with local Mixmaster dynamics

Cited by in corpus (12)

• Theorems on existence and global dynamics for the Einstein equations
• On the area of the symmetry orbits in $T^2$ symmetric spacetimes with Vlasov matter
• Asymptotic silence of generic cosmological singularities
• Spike Oscillations
• A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3
• Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes
• Areal Foliation and AVTD Behavior in T^2 Symmetric Spacetimes with Positive Cosmological Constant
• Weakly regular Einstein-Euler spacetimes with Gowdy symmetry. The global areal foliation
• Future asymptotics and geodesic completeness of polarized T2-symmetric spacetimes
• Structure of solutions near the initial singularity for the surface-symmetric Einstein-Vlasov system
• On initial conditions and global existence for accelerating cosmologies from string theory
• Stability of Asymptotic Behavior Within Polarised $T^2$-Symmetric Vacuum Solutions with Cosmological Constant