7 Singularity, Polarized Case

The proof of strong cosmic censorship, in the polarized as well as in the T3-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 S3 and S2 × S1 topology, the causal geodesics can be proven to be incomplete both to the future and to the past [21Jump To The Next Citation Point, p. 1673]. Thus, in those cases it is only necessary to analyze the singularities. In the case of T3-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 T3-Gowdy
 7.2 Associated Velocity Term Dominated system
 7.3 Asymptotics of the solution to the polarized T3-Gowdy equations
 7.4 Curvature blow up, polarized T3-case
 7.5 Asymptotic velocity, polarized T3-case
 7.6 S2 × S1 and S3 cases

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