标题： 球对称非均匀尘埃坍缩中的奇点结构 显示英文标题

标题： The Structure of Singularity in Spherical Inhomogeneous Dust Collapse

摘要： 我们在这里研究球对称非均匀尘埃引力坍缩中奇点形成的结构。 这种坍缩由Tolman-Bondi-Lemaître度规描述，这是爱因斯坦方程的一个两参数解族，由两个径向坐标的自由函数定义，即“质量函数”F(r)和“能量函数”f(r)。 这里的主要新结果以一般方式将黑洞和裸壳聚焦奇点的形成与其最终命运联系起来，这些奇点是这种坍缩的结果，与常规初始数据的一般形式相关。 这种数据通过物质的密度和速度分布来表征，在一个初始时间片上指定，坍缩从该时间片开始。 在本文开发的分析帮助下，研究了当奇点为裸露时它们的强度和稳定性问题。 特别是，可以看出，强曲率裸奇点可以从坍缩配置的初始密度分布的一般形式的初始数据中发展出来。 我们还在此建立，类似的结果也适用于黑洞的形成。 我们还讨论了为了避免壳交叉奇点以及壳聚焦裸奇点的初始数据的物理约束，从而确保坍缩必然以黑洞结束，保持宇宙审查猜想。 这些结果将一些早期关于非均匀尘埃坍缩的工作作为特例进行了推广，并提供了对引力坍缩中黑洞和裸奇点形成现象更清晰的洞察。 显示英文摘要

摘要： We study here the structure of singularity forming in gravitational collapse of spherically symmetric inhomogeneous dust. Such a collapse is described by the Tolman-Bondi-Lema{\^i}tre metric, which is a two-parameter family of solutions to Einstein equations, characterized by two free functions of the radial coordinate, namely the `mass function' F(r) and the `energy function' f(r). The main new result here relates, in a general way, the formation of black holes and naked shell-focusing singularities resulting as the final fate of such a collapse to the generic form of regular initial data. Such a data is characterized in terms of the density and velocity profiles of the matter, specified on an initial time slice from which the collapse commences. Several issues regarding the strength and stability of these singularities, when they are naked, are examined with the help of the analysis developed here. In particular, it is seen that strong curvature naked singularities can develop from a generic form of initial data in terms of the initial density profiles for the collapsing configuration. We also establish here that similar results hold for black hole formation as well. We also discuss here the physical constraints on the initial data for avoiding shell-crossing singularities; and also the shell-focusing naked singularities, so that the collapse will necessarily end as a black hole, preserving the cosmic censorship. These results generalize several earlier works on inhomogeneous dust collapse as special cases, and provide a clearer insight into the phenomena of black hole and naked singularity formation in gravitational collapse.