### 3.3 Existence of foliations, related symmetry classes

Let us, for the sake of completeness, mention some results concerning spacetimes satisfying
related symmetry conditions, in particular T^{2}-symmetry; see Section 2.2. That the maximal
globally-hyperbolic vacuum development of T^{2}-symmetric initial data is covered by areal coordinates is
proven in [9]. The result states that the area of the symmetry orbits exhausts for some
; whether or not is left open. However, this question has been addressed and
resolved in [51] and [91], see also [85]. In the context of areal coordinates, there is a fundamental
difference between the Gowdy case and the general T^{2}-symmetric case. In the Gowdy case,
the areal time coordinate is such that the metric is conformal to the Minkowski metric in the
-direction; see Equation (2). In the general T^{2}-symmetric case, this property is lost if one
insists on an areal time coordinate [9]. Results on the existence of areal coordinates covering
the MGHD in the case of solutions to the Einstein–Vlasov system with T^{3}-Gowdy symmetry
are contained in [4], see also [5], which treats solutions to the Einstein–Vlasov system in the
general T^{2}-symmetric case (the latter paper contains results concerning both areal and CMC
foliations). Existence of a CMC foliation under the assumption of the existence of two local Killing
vectors was demonstrated in [67], a paper, which generalizes, among other things, the results
of [49].