通过平坦时空拼接消除静态轴对称时空中的裸奇点
Removing naked singularities in static axially symmetric spacetimes by patching with the flat spacetimes
AI总结：
本文通过将Weyl类时空与平坦时空拼接，构造无裸奇点的静态轴对称时空，并证明在Curzon--Chazy和Zipoy--Voorhees外部时空中存在壳大小下界且满足相应能量条件。
摘要：
我们研究了通过将Weyl类时空与平坦时空拼接而构造的无裸奇点的静态轴对称时空。一旦外部几何被指定，衔接条件便决定了薄壳的形状（即两个被拼接时空之间的边界）以及该壳上能量和压强的分布，同时留下一个表示壳大小的自由参数。我们考察了壳外部由Curzon--Chazy或Zipoy--Voorhees时空给出的情形。在每种情形下，我们都找到了壳大小的下界。此外，我们发现弱能量条件和零能量条件对任意壳大小均得到满足，而主能量条件仅对足够大的壳得到满足。这些结果为具有非球对称外部且满足能量条件的非奇异时空提供了具体实例。
英文摘要：
We investigate static, axially symmetric spacetimes without naked singularities that are constructed by patching Weyl class spacetimes with the flat spacetimes. Once the exterior geometry is specified, the junction conditions determine the shape of a thin shell, which is the boundary between the two patched spacetimes, and the distribution of the energy and pressure on this shell, leaving a parameter representing the shell size free. We examine the cases where the exterior of the shell is given by Curzon--Chazy or Zipoy--Voorhees spacetimes. For each case, we find a lower bound on the shell size. Additionally, we find that the weak and null energy conditions are satisfied for any shell size, while the dominant energy condition is satisfied for sufficiently large shells. These results provide concrete examples of non-singular spacetimes with non-spherically symmetric exteriors that respect the energy conditions.
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。
