Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-12-19
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
21 pages, 7 figures
Scientific paper
We give a perturbative analysis for an infinitesimally thin cylindrical shell composed of counter rotating collisionless particles, originally devised by Apostolatos and Thorne. They found a static solution of the shell and concluded by C-energy argument that it is stable. Recently, the present authors and Ida reanalyzed this system by evaluating the C-energy on the future null infinity and found that the system has an instability, though it was not shown how the system is unstable. In this paper, it is shown in the framework of the linear perturbation theory that, if the constituent particles move slowly, the static shell is unstable in the sense that the perturbation of its circumferential radius oscillates with exponentially growing amplitude, whereas if the speed of the constituent particle exceeds a critical value, the shell just expands or contracts exponentially with time.
Kurita Yasunari
nakao Ken-ichi
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