The results we described in Section 8 and 9 consisted of constructions of solutions with certain types of
asymptotics. However, considering the formulation of the strong cosmic-censorship conjecture, it is of
interest to obtain conclusions given assumptions, which are phrased in terms of the initial data. The first
question to ask is if there is a condition on initial data, which ensures the existence of asymptotic
expansions. In [76], such a condition was established. Being phrased in terms of L^{2}-based energies, the
condition is rather technical. However, it does have the advantage of applying to higher dimensional
analogues of the equations (as opposed to much of the analysis to be described below). Other, less technical,
conditions were later established [12, 74]. Even though these results are of interest, they still only describe
a part of the dynamics (as the construction of spikes, see Section 9, demonstrates). The question then arises
concerning how to proceed. Considering the analysis in the polarized case, the asymptotic expansions
(37) – (38) and the spikes, it is clear that the velocity plays a central role. Thus, it is natural to
try to prove that it is possible to make sense of the concept of a velocity under more general
circumstances.

10.1 Existence of an asymptotic velocity

10.2 Relevance of the asymptotic velocity to the issue of curvature blow up

10.3 Interpretation of the asymptotic velocity as a rate of convergence to the boundary in hyperbolic space

10.4 Two dimensional version of the asymptotic velocity

10.5 Dominant contribution to the asymptotic velocity

10.6 Value of the asymptotic velocity as a criterion for the existence of expansions

10.2 Relevance of the asymptotic velocity to the issue of curvature blow up

10.3 Interpretation of the asymptotic velocity as a rate of convergence to the boundary in hyperbolic space

10.4 Two dimensional version of the asymptotic velocity

10.5 Dominant contribution to the asymptotic velocity

10.6 Value of the asymptotic velocity as a criterion for the existence of expansions

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