The necessary condition for the termination of families of radial causal geodesics at the naked shell focusing singularity in self-similar spherically symmetric spacetimes is worked out. The curvature growth along these geodesics is then examined and it is shown that strong curvature condition is satisfied along all radial non-spacelike geodesics escaping from the singularity.
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Dwivedi et al. (1991) studied this question.