Several problems and important questions are still left open. Perhaps the most important one is the issue of stability. A stability analysis is beyond the scope of this paper, but there is comment worth noting. Although there are indications for classical and semiclassical instabilities in various TM models , the robustness and effectiveness of these instabilities are still unclear. Further research is required in order to assess the robustness and effectiveness of the various instability phenomena. The model constructed here may provide a more solid basis for a systematic stability analysis. A few of its features that could be important for a genuine stability analysis include: (i) having a regular initial hypersurface, (ii) asymptotic flatness, and (iii) admitting a well-posed system of evolution equations. None of the previous TM models demonstrated all these properties. Two other important open questions should be mentioned here:
1. It may turn out that the evolving spacetime includes a black hole, and all CCCs are imprisoned inside the event horizon. In such a case the formation of CCCs might still have crucial implications to various aspects of the internal black-hole physics and geometry (e.g. singularity formation), but nevertheless the external universe will not be
influenced.
2. In our present construction, the initial data on S involve strong (though finite) gravitational fields. Is it possible to create a TM spacetime of this kind starting from weak-field initial data on some earlier initial hypersurface? Rephrasing this question: is it possible to create such a TM spacetime by sending weak gravitational waves (from past null infinity) and diluted dust shells (from past timelike infinity) in the inward direction?