  We numerically study the dynamics of an imploding hollow cylinder composed of
dust. Since there is no cylindrical black hole in 4-dimensional spacetime with
physically reasonable energy conditions, a collapsed dust cylinder involves a
naked singularity accompanied by its causal future, or a fatal singularity
which terminates the history of the whole universe. In a previous paper, the
present authors have shown that if the dust is assumed to be composed of
collisionless particles such that these particles go through the symmetry axis
of the cylinder, then the scalar polynomial singularity formed on the symmetry
axis is so weak that almost all of geodesics are complete, and thus effectively
no singularity forms by the collapse of a hollow dust cylinder. By contrast, in
this paper, we assume that whole of the collapsed dust settles down on the
symmetry axis by changing its equation of state. Obtained solutions are the
straightforward extension of Morgan's null dust solution, in which no
gravitational radiation is emitted. However, in the present case with timelike
dust, infinite amount of $C$-energy initially stored in the system is released
through gravitational radiation. We also show that the gravitational waves
asymptotically behave in a self-similar manner.
