3D Simulation of Spindle Gravitational Collapse of a Collisionless Particle System
3D Simulation of Spindle Gravitational Collapse of a Collisionless Particle System
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无碰撞粒子系统主轴重力塌缩的 3D 模拟
DOI：
10.1088/1361-6382/aa6ad5
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Hirotada Okawa
中科院分区：
文献类型：
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作者：
Chul-Moon Yoo;Tomohiro Harada;Hirotada Okawa
我们用三维数值相对论程序模拟了无碰撞粒子系统的纺锤引力崩塌，并将定性结果与Shapiro和Teukolsky(ST)(1991 Phys.莱特牧师。66 994)。模拟从颗粒的长椭圆形分布开始，观察到纺锤形的崩塌。在时间演化过程中，对曲率不变量的峰值及其空间位置进行监测。我们发现，Kretschmann不变量的峰值在没有视界的某个时刻达到最大值，并且随着分辨率的提高，其峰值更大，这与ST。对于Weyl曲率不变量，我们也发现了类似的趋势。因此，我们的结果支持在无限分辨率极限下，无碰撞粒子系统的轴对称纺锤形坍缩导致裸奇点的形成。然而，与ST不同的是，我们的代码不会在那时崩溃，而是远远超出它的范围。我们发现，在一定时间内，曲率不变量的峰值开始随时间逐渐减小。与ST的另一个显著区别是，在我们的例子中，Kretschmann曲率不变量的峰值位置总是在物质分布的内部。
We simulate the spindle gravitational collapse of a collisionless particle system in a 3D numerical relativity code and compare the qualitative results with the old work done by Shapiro and Teukolsky (ST)(1991 Phys. Rev. Lett. 66 994). The simulation starts from the prolate-shaped distribution of particles and a spindle collapse is observed. The peak value and its spatial position of curvature invariants are monitored during the time evolution. We find that the peak value of the Kretschmann invariant takes a maximum at some moment, when there is no apparent horizon, and its value is greater for a finer resolution, which is consistent with what is reported in ST. We also find a similar tendency for the Weyl curvature invariant. Therefore, our results lend support to the formation of a naked singularity as a result of the axially symmetric spindle collapse of a collisionless particle system in the limit of infinite resolution. However, unlike in ST, our code does not break down then but goes well beyond. We find that the peak values of the curvature invariants start to gradually decrease with time for a certain period of time. Another notable difference from ST is that, in our case, the peak position of the Kretschmann curvature invariant is always inside the matter distribution.