  We investigate an infinitesimally thin cylindrical shell composed of
counter-rotating dust particles. This system was studied by Apostolatos and
Thorne in terms of the C-energy for a bounded domain. In this paper, we
reanalyze this system by evaluating the C-energy on the future null infinity.
We find that some class of momentarily static and radiation-free initial data
does not settle down into static, equilibrium configurations, and otherwise
infinite amount of the gravitational radiation is emitted to the future null
infinity. Our result implies the existence of an instability in this system. In
the framework of the Newtonian gravity, a cylindrical shell composed of
counter-rotating dust particles can be in a steady state with oscillation by
the gravitational attraction and centrifugal repulsion, and hence a static
state is not necessarily realized as a final state. By contrast, in the
framework of general relativity, the steady oscillating state will be
impossible since the gravitational radiation will carry the energy of the
oscillation to infinity. Thus, this instability has no counterpart in the
Newtonian gravity.
