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 , such a condition was established. Being phrased in terms of L2-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.
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