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 (35) 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 . Consider a
past inextendible causal curve . Due to the form of the metric (2), it is clear that the -coordinate of
this curve has to converge in the direction towards the singularity. Call the limiting value . Then,
the Kretschmann scalar is unbounded along 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 [50, Theorem IV.1, p. 105].