标题： 球形黑洞内部的均匀类空奇点 显示英文标题

标题： Homogeneous spacelike singularities inside spherical black holes

摘要： 最近的数值模拟发现，当被一个自引力、最小耦合、无质量、球对称的标量场非线性扰动时，球对称带电黑洞内部的柯西视界在晚期时间会变成一个类光弱奇点，该奇点单调地聚焦到$r=0$，此时奇点变为类空。我们的主要目标是研究这个类空奇点。我们分析地研究了在奇点附近球对称的爱因斯坦-麦克斯韦-标量方程。我们在均匀性的简化假设下，获得了在$r=0$附近度规函数和标量场的级数展开解。即，我们忽略了空间导数，只保留时间导数。我们发现确实存在一个通用的类空奇点解（从解依赖足够多的自由参数的意义上来说），其性质与数值模拟中发现的类似。这种奇点在Tipler意义上是强烈的，即每个扩展物体都会不可避免地被压成零体积。从这个意义上说，这是一种类似于不带电球对称黑洞内部的类空奇点。另一方面，这两种情况之间有一些重要的差异。我们的模型也可以推广到更一般的非均匀情况。在更现实的模型（如旋转黑洞与引力扰动耦合）中是否会出现相同类型的奇点，仍然是一个开放问题。 显示英文摘要

摘要： Recent numerical simulations have found that the Cauchy horizon inside spherical charged black holes, when perturbed nonlinearly by a self-gravitating, minimally-coupled, massless, spherically-symmetric scalar field, turns into a null weak singularity which focuses monotonically to $r=0$ at late times, where the singularity becomes spacelike. Our main objective is to study this spacelike singularity. We study analytically the spherically-symmetric Einstein-Maxwell-scalar equations asymptotically near the singularity. We obtain a series-expansion solution for the metric functions and for the scalar field near $r=0$ under the simplifying assumption of homogeneity. Namely, we neglect spatial derivatives and keep only temporal derivatives. We find that there indeed exists a generic spacelike singularity solution for these equations (in the sense that the solution depends on enough free parameters), with similar properties to those found in the numerical simulations. This singularity is strong in the Tipler sense, namely, every extended object would inevitably be crushed to zero volume. In this sense this is a similar singularity to the spacelike singularity inside uncharged spherical black holes. On the other hand, there are some important differences between the two cases. Our model can also be extended to the more general inhomogeneous case. The question of whether the same kind of singularity evolves in more realistic models (of a spinning black hole coupled to gravitational perturbations) is still an open question.