### 4.4 Pathological examples in the case of Gowdy

Before ending this section, let us record the existence of pathological behavior in the class of
Gowdy spacetimes. The most obvious example is provided by the flat Kasner solution; letting
in Equation (4) leads to the metric
Viewing this metric on ,

yields an isometry to a subset of Minkowski space. Consequently, is flat, and we shall refer to
as the flat Kasner solution. This solution is past causally geodesically incomplete, but
the curvature is clearly bounded. Furthermore, it is extendible. Considering the same solution on the torus,
it is also possible to construct an extension; see, e.g., [82].

However, there are more sophisticated examples of pathologies. In [20], the authors demonstrate that
given any positive integer , there is a polarized Gowdy vacuum spacetime with at least inequivalent
maximal extensions.