标题： 壳层塌缩至预存黑洞的精确解 显示英文标题

标题： Exact solutions for shells collapsing towards a pre-existing black hole

摘要： 恒星的引力坍缩对于广义相对论和天体物理学来说都是一个重要问题，它与著名的“冻结恒星”悖论密切相关。 这个悖论已被广泛讨论，并似乎在共动坐标系中得到了解决。 然而，对于一个真实天体物理观测者而言，在有限时间内，这个问题应从远处静止观测者的角度来讨论，这也是本文的主要目的。 基于奥本海默和斯奈德（1939年）的经典工作，我们提出了一个或两个尘埃壳向预存黑洞坍缩的精确解。 我们发现，壳内区域的度规是时间相关的，且随着壳向预存黑洞坍缩，壳内的时钟变得越来越慢。 这意味着壳的内区域受到壳本身属性的影响，这与牛顿理论的结果相反。 这并不违背毕晓普定理，因为在我们的案例中，为了确保度规的连续性，我们不能随意选择壳内部的时钟。 原则上，如果一束光穿过壳，则这一结果可能通过实验进行验证，这将比没有壳的情况下需要更长的时间。 它可以被视为广义的夏皮罗效应，因为这种效应是由外部的质量引起的，而不是标准夏皮罗效应中的内部质量。 我们还发现，在真实的天体物理环境中，根据外部观察者的时钟，物质确实可以穿越黑洞的视界，并不会在黑洞的事件视界附近积累，即对于外部观察者而言，不会形成所谓的“冻结恒星”。 显示英文摘要

摘要： The gravitational collapse of a star is an important issue both for general relativity and astrophysics, which is related to the well known "frozen star" paradox. This paradox has been discussed intensively and seems to have been solved in the comoving-like coordinates. However, to a real astrophysical observer within a finite time, this problem should be discussed in the point of view of the distant rest-observer, which is the main purpose of this paper. Following the seminal work of Oppenheimer and Snyder (1939), we present the exact solution for one or two dust shells collapsing towards a pre-existing black hole. We find that the metric of the inner region of the shell is time-dependent and the clock inside the shell becomes slower as the shell collapses towards the pre-existing black hole. This means the inner region of the shell is influenced by the property of the shell, which is contrary to the result in Newtonian theory. It does not contradict the Birkhoff's theorem, since in our case we cannot arbitrarily select the clock inside the shell in order to ensure the continuity of the metric. This result in principle may be tested experimentally if a beam of light travels across the shell, which will take a longer time than without the shell. It can be considered as the generalized Shapiro effect, because this effect is due to the mass outside, but not inside as the case of the standard Shapiro effect. We also found that in real astrophysical settings matter can indeed cross a black hole's horizon according to the clock of an external observer and will not accumulate around the event horizon of a black hole, i.e., no "frozen star" is formed for an external observer as matter falls towards a black hole. (abridged)