New instability in relativistic cylindrically symmetric system

Abstract

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.

16 pages, no figure

References in corpus (5)

• Asymptotic Structure of Symmetry Reduced General Relativity
• Observation of Incipient Black Holes and the Information Loss Problem
• Gravitational waves, black holes and cosmic strings in cylindrical symmetry
• Behavior of Einstein-Rosen Waves at Null Infinity
• Border of Spacetime

Cited by in corpus (5)

• Cylindrical Systems in General Relativity
• Einstein-Rosen waves and the self-similarity hypothesis in cylindrical symmetry
• Visible borders of spacetime generated by high-energy collisions
• The effect of radiative gravitational modes on the dynamics of a cylindrical shell of counter rotating particles
• On the evolution of the momentarily static radiation free data in the Apostolatos - Thorne cylindrical shell model