无限厚片与其它常正密度奇异平面对称时空
Infinite slabs and other weird plane symmetric space-times with constant positive density
摘要：
本文给出了在$z=0$下方具有恒定正密度的静态平面对称物质分布的爱因斯坦方程的精确解。该解基本上取决于两个常数：密度$ρ$和参数$κ$。我们表明，这个时空在有限深度的内部奇点处结束。我们将此解与真空解相匹配，并根据板的参数计算外部引力场。根据$κ$的值，这些板可以是吸引的、排斥的或中性的。在第一种情况下，时空也在另一个奇点上结束。在其他情况下，当$z\to\infty$。我们还找到了解决方案，包括加入一个有吸引力的板和排斥的，和两个中性的。我们还讨论了如何通过在两个这样的平板之间插入一片真空来组装一个“引力电容器”。
英文摘要：
We present the exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with constant positive density located below $z=0$. This solution depends essentially on two constants: the density $ρ$ and a parameter $κ$. We show that this space-time finishes down below at an inner singularity at finite depth. We match this solution to the vacuum one and compute the external gravitational field in terms of slab's parameters. Depending on the value of $κ$, these slabs can be attractive, repulsive or neutral. In the first case, the space-time also finishes up above at another singularity. In the other cases, they turn out to be semi-infinite and asymptotically flat when $z\to\infty$. We also find solutions consisting of joining an attractive slab and a repulsive one, and two neutral ones. We also discuss how to assemble a "gravitational capacitor" by inserting a slice of vacuum between two such slabs.
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