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arXiv 2102.05987gr-qc
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可扩展外壳:跨越空边界的一般匹配和剪切粘贴形式主义的连接

Null shells: general matching across null boundaries and connection with cut-and-paste formalism

M. Manzano, M. Mars

摘要:

薄壳是研究无限薄的无质量粒子或脉冲波传播的一种有用的几何构造。本文确定并研究了两个以各自的零嵌入超曲面为边界的时空匹配的充要条件。只要匹配是可能的,它示出依赖于一组零生成器在每个边界和一个标量函数,称为阶跃函数,它确定沿零生成器的点的移位之间的一个同构。一般来说,最多存在一个可能的匹配,但在某些情况下并非如此。当零边界是全测地线时,它们之间的点对点识别引入了一个自由度,其性质和后果进行了详细的分析。导出了一般零壳的能量动量张量的表达式。最后,我们找到了最一般的壳(非零能量,能流和压力),可以通过匹配两个闵可夫斯基区域跨越零超平面。这使我们能够展示原始彭罗斯的剪切和粘贴结构如何与标准匹配形式主义相适应和连接。

英文摘要:

Null shells are a useful geometric construction to study the propagation of infinitesimally thin concentrations of massless particles or impulsive waves. In this paper, we determine and study the necessary and sufficient conditions for the matching of two spacetimes with respective null embedded hypersurfaces as boundaries. Whenever the matching is possible, it is shown to depend on a diffeomorphism between the set of null generators in each boundary and a scalar function, called step function, that determines a shift of points along the null generators. Generically there exists at most one possible matching but in some circumstances this is not so. When the null boundaries are totally geodesic, the point-to-point identification between them introduces a freedom whose nature and consequences are analyzed in detail. The expression for the energy-momentum tensor of a general null shell is also derived. Finally, we find the most general shell (with non-zero energy, energy flux and pressure) that can be generated by matching two Minkowski regions across a null hyperplane. This allows us to show how the original Penrose's cut-and-paste construction fits and connects with the standard matching formalism.

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