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

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

2003-04-04

arxiv.org/abs/gr-qc/0304019v3

Class.Quant.Grav. 20 (2003) 3783-3796

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

The appendix which appears in version 1 has a technical problem (the inequality appearing as the first stage of (52) is not ne

Scientific paper

10.1088/0264-9381/20/16/316

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.

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