广义相对论无限平面
The general relativistic infinite plane
摘要：
均匀场是静电学或牛顿引力的入门课程中最简单和最有用的例子之一。在广义相对论中，关于什么是均匀场，有几种说法。在这篇文章中，我们研究两个度量，可以被认为是广义相对论版本的无限平面与有限的质量每单位面积。第一个度量是5D“膜”世界模型的4D版本，这是许多当前研究论文的起点。第二种情况是宇宙畴壁度规。我们检验这些不同的度量在多大程度上符合或偏离我们关于无限平面的引力场的牛顿直觉。这些解为广义相对论的初学者提供了计算实践和对爱因斯坦场方程的概念性理解。此外，他们通过向学生介绍处于当前研究前沿的材料来做到这一点。
英文摘要：
Uniform fields are one of the simplest and most pedagogically useful examples in introductory courses on electrostatics or Newtonian gravity. In general relativity there have been several proposals as to what constitutes a uniform field. In this article we examine two metrics that can be considered the general relativistic version of the infinite plane with finite mass per unit area. The first metric is the 4D version of the 5D "brane" world models which are the starting point for many current research papers. The second case is the cosmological domain wall metric. We examine to what extent these different metrics match or deviate from our Newtonian intuition about the gravitational field of an infinite plane. These solutions provide the beginning student in general relativity both computational practice and conceptual insight into Einstein's field equations. In addition they do this by introducing the student to material that is at the forefront of current research.
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