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arXiv 0811.1634gr-qc
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第一类物质空心球的高速坍缩

High-Speed Collapse of a Hollow Sphere of Type I Matter

Zahid Ahmad, Tomohiro Harada, Ken-ichi Nakao, M. Sharif

摘要:

本文研究了空心球物质以极大初速度坍缩的动力学。时空最初非常类似于Vaidya解决方案,从这个背景的偏差被微扰处理。假设径向压力$p_{\rm R}=kρ$和切向压力$p_{\rm T}=wρ$的状态方程为常数$k$和$w$。我们发现,对于状态方程$k< 1$和$0<w\leq1$的情况下,初速度,这是接近光速,强烈减速。这一结果表明,即使在初始接近光速的坍缩中,压力对引力坍缩中奇点的形成也是必不可少的。相反,在负切向压力的情况下,本结果意味着,即使径向压力为正,弱、强和主导能量条件成立,也可以形成类似于Vaidya时空的中心裸奇点。特别是在$w<-(1-k)/4$中,高速坍缩将产生与Vaidya时空非常相似的时空结构。

英文摘要:

In this paper, we study the dynamics of a hollow spherical matter collapsing with very large initial velocity. The spacetime is initially very similar to the Vaidya solution, and the deviations from this background are treated perturbatively. The equations of state for radial pressure $p_{\rm R}=kρ$ and tangential one $p_{\rm T}=wρ$ with constant $k$ and $w$ are assumed. We find for the case of equations of state $k< 1$ and $0<w\leq1$ that the initial velocity, which is nearly the speed of light, is strongly decelerated. This result implies that the pressure is essential to the property of singularity formation in gravitational collapse even for initially nearly light-speed collapse. By contrast, in cases with the negative tangential pressure, the present result implies that the central naked singularity similar to that of the Vaidya spacetime can be formed, even though the radial pressure is positive, and the weak, strong and dominant energy conditions hold. Especially, in the case of $w<-(1-k)/4$, the high-speed collapse will produce the spacetime structure very similar to that of the Vaidya spacetime.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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