标题： 球对称时空中的无穷远点的投影路径 显示英文标题

标题： Projective path to points at infinity in spherically symmetric spacetimes

摘要： 本文证明了，在一个四维球对称时空流形中，可以考虑由分数线性映射表示的坐标变换，这些变换产生了等距，并且是用于将无穷远点化为有限距离的最简单的坐标变换示例。 所研究的球对称时空的射影边界是三个点的不相交并集：未来类时无穷远点、过去类时无穷远点、类空无穷远点，以及半直线与二维球面的三维乘积。 接着，在以施瓦西时空的射影变换坐标 \$(t',r',\theta',\phi')\$ 研究测地线时，特别关注它们接近我们定义的无穷远点的方式。 接下来，使用我们的射影方法研究了Nariai、de Sitter和Gödel时空。 由于这里定义的无穷远点类型仅依赖于时空流形中的对称性，因此它们具有广泛的应用范围，这激发了对施瓦西、Nariai、de Sitter和Gödel时空的创新分析。 显示英文摘要

摘要： This paper proves that, in a four-dimensional spherically symmetric spacetime manifold, one can consider coordinate transformations expressed by fractional linear maps which give rise to isometries and are the simplest example of coordinate transformation used to bring infinity down to a finite distance. The projective boundary of spherically symmetric spacetimes here studied is the disjoint union of three points: future timelike infinity, past timelike infinity, spacelike infinity, and the three-dimensional products of half-lines with a 2-sphere. Geodesics are then studied in the projectively transformed (t',r',theta',phi') coordinates for Schwarzschild spacetime, with special interest in their way of approaching our points at infinity. Next, Nariai, de Sitter and Godel spacetimes are studied with our projective method. Since the kinds of infinity here defined depend only on the symmetry of interest in a spacetime manifold, they have a broad range of applications, which motivate the innovative analysis of Schwarzschild, Nariai, de Sitter and Godel spacetimes.