### 1.2 Outline, the asymptotics in the direction towards the singularity

Asymptotic behavior in the direction of the singularity in the polarized case. The two Gowdy
cases in which results concerning strong cosmic censorship exist are the polarized case and the general
T^{3}-case. In Section 7, we focus on the polarized case. In particular, on finding asymptotic expansions
of the metric components in the direction towards the singularity. One function appearing in
the expansions has a special importance. From the wave-map point of view, it has a natural
interpretation as the rate at which the solution tends to the boundary of hyperbolic space; see
Section 7.4. As a consequence, it is referred to as the asymptotic velocity. Beyond having a natural
interpretation, the asymptotic velocity has an additional important property. In fact, it can be
used as a criterion for curvature blow up along causal curves going into the singularity; see
Section 7.5.
Existence of solutions with specified asymptotics, Fuchsian methods. Due to the central
importance of the asymptotic expansions in the polarized case, it is of interest to obtain expansions in the
general T^{3}-case. One way to proceed is to try to construct solutions with prescribed asymptotics. This is
the subject of Section 8. Again, it is possible to define the concept of an asymptotic velocity. It has the
same geometric interpretation and importance as in the polarized case. The results on existence of
expansions depend on a restriction of the asymptotic velocity. We describe the results and motivate the
restriction.

Spikes. The numerical studies indicate that for most spatial points, the asymptotic expansions
presented in Section 8 constitute a good description of the asymptotics. However, they also indicate that
there are spatial points where the behavior is very different. Due to the visual impression of plots of
the solutions in the neighborhood of the exceptional points, the corresponding features have
been referred to as “spikes”. In Section 9, we describe analytic constructions of solutions with
spikes.

Existence of an asymptotic velocity in the general T^{3}-Gowdy case. The analysis in the
polarized case and the construction of solutions with prescribed asymptotics indicate the importance of the
asymptotic velocity. Consequently, it is of interest to prove that the asymptotic velocity exists in general.
This is the subject of Section 10. We also demonstrate that the asymptotic velocity can be viewed as a
two-dimensional object in the disc model. Finally, we illustrate that it can be used as a criterion for the
existence of expansions.

Definition of the generic set in the general T^{3}-Gowdy case. As a preparation for the
formulation of the theorem verifying that strong cosmic censorship holds in T^{3}-Gowdy, we define the
generic set of initial data in Section 11.