For the sake of completeness, let us also recall the definition of C2-inextendibility.
Definition 9 Let be a connected Lorentz manifold, which is at least C2. Assume there is a connected C2 Lorentz manifold of the same dimension as and an isometric embedding such that . Then is said to be C2-extendible. If is not C2-extendible, it is said to be C2-inextendible.
It might be possible to obtain this result using different methods. In fact, let be the set of initial data such that the corresponding solutions have an asymptotic velocity, which is different from one on a dense subset of the singularity. Endowing the initial data with the -topology, it is possible to show that is a dense set . Due to its definition, it is clear that solutions corresponding to initial data in have the property that the curvature blows up on a dense subset of the singularity. It would be natural to expect the corresponding solutions to be inextendible, but providing a proof is nontrivial. Important steps in the direction of proving this statement were taken in . However, to the best of our knowledge, there is, as yet, no result to this effect.
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