Szekeres模型的物理和几何解释
Physical and Geometrical Interpretation of the epsilon <= 0 Szekeres Models
摘要：
本文研究了拟伪球和拟平面Szekeres模型的性质和行为，得到了正则性条件，并分析了它们的结果。在准球形情况下，与“半径”和“质量”相关的量必须以不同的方式理解。具有伪球形叶理的模型可以有空间极大值和极小值，但没有原点。“质量”和“半径”函数可以是一个增加和一个减少，而不引起壳交叉。这种情况最自然地描述了一个蛇形的，密度变化的空隙在一个更温和地变化的不均匀的背景，虽然区域发展过密度也是可能的。具有平面叶理的Szekeres模型既不能有空间极值也不能有空间原点，不能是空间平坦的，并且它们不能比相应的Ellis模型具有更多的不均匀性，但是平面表面可以是球形和伪球形叶理区域之间的边界。
英文摘要：
We study the properties and behaviour of the quasi-pseudospherical and quasi-planar Szekeres models, obtain the regularity conditions, and analyse their consequences. The quantities associated with "radius" and "mass" in the quasi-spherical case must be understood in a different way for these cases. The models with pseudospherical foliation can have spatial maxima and minima, but no origins. The "mass" and "radius" functions may be one increasing and one decreasing without causing shell crossings. This case most naturally describes a snake-like, variable density void in a more gently varying inhomogeneous background, although regions that develop an overdensity are also possible. The Szekeres models with plane foliation can have neither spatial extrema nor origins, cannot be spatially flat, and they cannot have more inhomogeneity than the corresponding Ellis model, but a planar surface can be the boundary between regions of spherical and pseudospherical foliation.
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