Abstract

Starting from a general transformation for spherically symmetric metrics where g_11=-1/g_00, we analyze coordinates with the common property of conformal flatness at constant solid angle element. Three general possibilities arise: one where tortoise coordinate appears as the unique solution, other that includes Kruskal-Szekeres coordinates as a very specific case, but that also allows other similar transformations, and finally a new set of coordinates with very different properties than the other two. In particular, it represents any causal patch of the spherically symmetric metrics in a compactified form. We analyze general properties of the new proposed “pulsating coordinates”, and then proceed to apply the transformation for the Schwarzschild spacetime, as well as for several cosmological solutions, contrasting properties with the Kruskal case. In particular, Anti-de-Sitter solution presents interesting features.

中文翻译：

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超越史瓦西：球对称度量的新脉动坐标

摘要

从球对称度量的一般变换（其中 g_11=-1/g_00）开始，我们分析具有恒定立体角元素的共形平坦度的共同属性的坐标。出现三种常见的可能性：一种是乌龟坐标作为唯一的解决方案，另一种是将 Kruskal-Szekeres 坐标作为一种非常具体的情况，但也允许其他类似的变换，最后是一组与其他坐标具有非常不同属性的新坐标二。特别是，它以紧凑的形式表示球对称度量的任何因果补丁。我们分析了新提出的“脉动坐标”的一般性质，然后继续将变换应用于史瓦西时空以及几个宇宙学解决方案，并将性质与克鲁斯卡尔情况进行对比。特别是，Anti-de-Sitter 解决方案呈现出有趣的功能。