3.2 Areal foliation
In the case of T3-Gowdy spacetimes, there is another natural foliation; considering Equation (2), it is
clear that the area of the symmetry orbits are proportional to the time coordinate . Consequently, such a
time coordinate is referred to as an areal time coordinate. It is natural to ask if the areal time coordinate
exhausts the interval . That the answer is yes in the case of vacuum T3-Gowdy was
demonstrated by Moncrief . Furthermore, he verified that the foliation covers the entire MGHD.
However, since the starting point of the argument in  is a constant- hypersurface, it is of
interest to note that the results of  yield the same conclusions starting with a general Cauchy