Dynamical Instability in a Relativistic Cylindrical Shell Composed of Counter-Rotating Particles
Dynamical Instability in a Relativistic Cylindrical Shell Composed of Counter-Rotating Particles
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由反向旋转粒子组成的相对论圆柱壳的动力学不稳定性
DOI：
10.1143/ptp.128.191
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
K. Nakao
中科院分区：
文献类型：
--
作者：
Yasunari Kurita;K. Nakao
我们对一个由反旋转无碰撞粒子组成的极薄圆柱壳进行了微扰分析，该壳最初是由Apostolatos和Thorne设计的，他们发现了壳的静态解，并通过c -能量论证得出壳是稳定的。最近，作者和Ida通过评估未来零无穷上的c能量对该系统进行了重新分析，发现该系统表现出不稳定性，尽管没有说明系统是如何不稳定的。本文在线性摄动理论的框架下表明，如果组成粒子运动缓慢，则静态壳是不稳定的，即其圆周半径的摄动以指数增长的振幅振荡，而如果组成粒子的速度超过临界值，则出现表现为指数膨胀或收缩的不稳定模式。目前的结果反驳了Apostolatos和Thorne猜想的证据，该猜想认为旋转会阻止纺锤体引力坍缩，并且似乎支持Shapiro和Teukolsky关于纺锤体坍缩的数值结果。他们的数值结果是否暗示裸奇点的形成仍然存在争议。然而，如果主轴引力坍缩真的导致裸奇点的形成，我们的结果意味着对宇宙审查猜想的违反。主题索引：451
We perform a perturbative analysis of an infinitesimally thin cylindrical shell composed of counter-rotating collisionless particles, originally devised by Apostolatos and Thorne, who found a static solution of the shell and concluded by C-energy argument that it is stable. Recently, the present authors and Ida have reanalyzed this system by evaluating the C-energy on the future null infinity and found that the system shows instability, although 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 constituent particles move slowly, the static shell is unstable in the sense that the perturbation of its circumferential radius oscillates with an exponentially growing amplitude, whereas if the speed of the constituent particle exceeds a critical value, unstable modes exhibiting exponential expansion or contraction of the shell appear. The present result disproves the evidence for the conjecture of Apostolatos and Thorne, which states that rotation halts the spindle gravitational collapse, and seems to support the numerical results on the spindle collapse obtained by Shapiro and Teukolsky. It is still controversial whether their numerical results imply the formation of naked singularities. However, if the spindle gravitational collapse really results in the formation of naked singularities, our result implies a violation of the cosmic censorship conjecture. Subject Index: 451
DOI：
10.1017/9781009253161
发表时间：
2023-02
期刊：
--
影响因子：
--
作者：
S. Hawking;G. Ellis
通讯作者：
S. Hawking;G. Ellis