标题： 薄壳模型的重新审视 显示英文标题

标题： Thin shell model revisited

摘要： 我们重新考虑了薄壳模型的一些基本问题。 首先，我们指出“剪切和粘合”构造不能保证一个定义良好的流形，因为壳两侧的坐标没有重叠。 当要求薄壳两侧的时空度规是连续的时候，这也提供了一种指定切空间和流形的方法。 其他作者已经证明，这种指定在壳碰撞时会导致守恒定律。 另一方面，众所周知的面积半径$r$看起来像是一个能覆盖球对称时空所有区域的完美坐标。 然而，我们通过简单但严格的论证表明，如果壳两侧的度规是连续的，$r$无法成为薄壳附近区域的坐标。 当两个球形壳碰撞并合并成一个时，我们证明$r$仍然可能是一个好的坐标，并且守恒定律成立。 为了实现这一点，由壳分隔的不同时空区域必须以特定方式粘合，使得某些约束得到满足。 我们通过数值求解约束条件，将我们的新构造与旧构造进行了比较。 显示英文摘要

摘要： We reconsider some fundamental problems of the thin shell model. First, we point out that the "cut and paste" construction does not guarantee a well-defined manifold because there is no overlap of coordinates across the shell. When one requires that the spacetime metric across the thin shell is continuous, it also provides a way to specify the tangent space and the manifold. Other authors have shown that this specification leads to the conservation laws when shells collide. On the other hand, the well-known areal radius $r$ seems to be a perfect coordinate covering all regions of a spherically symmetric spacetime. However, we show by simple but rigorous arguments that $r$ fails to be a coordinate covering a neighborhood of the thin shell if the metric across the shell is continuous. When two spherical shells collide and merge into one, we show that it is possible that $r$ remains to be a good coordinate and the conservation laws hold. To make this happen, different spacetime regions divided by the shells must be glued in a specific way such that some constraints are satisfied. We compare our new construction with the old one by solving constraints numerically.