标题： 相对论柱对称系统中的新不稳定性 显示英文标题

标题： New instability in relativistic cylindrically symmetric system

摘要： 我们研究一个由反向旋转的尘埃粒子组成的无限薄圆柱壳。 该系统由Apostolatos和Thorne在有限区域的C能量方面进行了研究。 在本文中，我们通过在未来的类光无穷远处评估C能量来重新分析该系统。 我们发现，某些瞬时静态且无辐射的初始数据不会趋于静态平衡配置，而是会向未来的类光无穷远处发出无限量的引力辐射。 我们的结果表明该系统中存在不稳定性。 在牛顿引力框架下，由反向旋转的尘埃粒子组成的圆柱壳可以通过引力吸引和离心排斥达到稳态振荡，因此静态状态并不一定作为最终状态出现。 相比之下，在广义相对论框架下，稳定振荡状态是不可能的，因为引力辐射会将振荡的能量带到无限远。 因此，这种不稳定性在牛顿引力中没有对应物。 显示英文摘要

摘要： 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.