The proof of strong cosmic censorship, in the polarized as well as in the T^{3}-Gowdy case, proceeds via
Conjecture 2. In other words, it consists of a proof of the fact that, generically, the curvature is unbounded
in the incomplete directions of causal geodesics. In the polarized case with S^{3} and S^{2} × S^{1} topology, the
causal geodesics can be proven to be incomplete both to the future and to the past [21, p. 1673]. Thus, in
those cases it is only necessary to analyze the singularities. In the case of T^{3}-Gowdy, there is an expanding
direction, and it is necessary to prove that causal geodesics are complete in that direction. In general, it is
thus necessary to analyze the behavior in the direction towards the singularity and the behavior in the
expanding direction. Since the methods involved are very different, we shall consider the two cases
separately. Furthermore, since the analysis in the polarized and general cases are quite different,
we shall begin by describing the analysis in the direction towards the singularity in polarized
Gowdy.

7.1 Equations, polarized T^{3}-Gowdy

7.2 Associated Velocity Term Dominated system

7.3 Asymptotics of the solution to the polarized T^{3}-Gowdy equations

7.4 Curvature blow up, polarized T^{3}-case

7.5 Asymptotic velocity, polarized T^{3}-case

7.6 S^{2} × S^{1} and S^{3} cases

7.2 Associated Velocity Term Dominated system

7.3 Asymptotics of the solution to the polarized T

7.4 Curvature blow up, polarized T

7.5 Asymptotic velocity, polarized T

7.6 S

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