7.4 Curvature blow up, polarized T3-case

From the point of view of proving strong cosmic censorship, the main reason for wanting to derive expansions of the form of Equation (35View Equation) is that they can be used to prove curvature blow up. It turns out that criteria for curvature blow up and the absence thereof can be formulated in terms of v. Consider a past inextendible causal curve γ. Due to the form of the metric (2View Equation), it is clear that the 𝜃-coordinate of this curve has to converge in the direction towards the singularity. Call the limiting value 𝜃0. Then, if

the Kretschmann scalar is unbounded along γ in the direction of the singularity. Otherwise, it is bounded. This result, as well as quantitative estimates for the rate at which the curvature tends to infinity, is contained in [50Jump To The Next Citation Point, Theorem IV.1, p. 105].

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