always exists due to [79, Lemma 6.17, p. 1011] (as an aside, it is worth noting that is a real analytic function from the open unit disc to the real numbers if is the hyperbolic distance from the origin of the unit disc to ; see [79, Remark 6.18, p. 1011]). It would be reasonable to call this limit, which we shall refer to as , the velocity, since it contains information not only concerning size, but also concerning direction. However, the most important aspect of this construction is that it is two-dimensional. An essential step of the proof of strong cosmic censorship is to perturb away from zero velocity. In the case of polarized Gowdy, this is not possible. However, if the velocity is a two-dimensional object, it is at least potentially possible.
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