We obtain a global existence result for the Einstein equations. We show that
in the maximal Cauchy development of vacuum T2 symmetric initial data with
nonvanishing twist constant, except for the special case of flat Kasner initial
data, the area of the T2 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.Comment: The 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 correcte