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 evaluati
ng 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.
The topological structure of the event horizon has been investigated in terms of the Morse theory. The elementary process of topological evolution can be understood as a handle attachment. It has been found that there are certain constraints on the n
ature of black hole topological evolution: (i) There are n kinds of handle attachments in (n+1)-dimensional black hole space-times. (ii) Handles are further classified as either of black or white type, and only black handles appear in real black hole space-times. (iii) The spatial section of an exterior of the black hole region is always connected. As a corollary, it is shown that the formation of a black hole with an S**(n-2) x S**1 horizon from that with an S**(n-1) horizon must be non-axisymmetric in asymptotically flat space-times.
