Kruskal Dynamics for Radial Geodesics

• 作者: Abhas Mitra
• 来源期刊: 天文学与天体物理学国际期刊(英文)
• 学科: 数学
• 关键词: Black HOLE Kruskal COORDINATES SPACETIME SINGULARITY
• 年，卷（期）: 2012,（3）
• 页码范围: 174-179
• 页数: 6页
• 分类号: O1

摘要

The total spacetime manifold for a Schwarzschild black hole (BH) is believed to be described by the Kruskal coordi-nates and , where r and t are the conventional Schwarzschild radial and time coordinates re-spectively. The relationship between r and t for a test particle moving along a radial or non-radial geodesic is well known. Similarly, the expression for the vacuum Schwarzschild derivative for a geodesic, in terms of the constants of motion, is well known. However, the same is not true for the Kruskal coordinates;and, we derive here the expression for the Kruskal derivative for a radial geodesic in terms of the constants of motion. In particular, it is seen that the value of ) is regular on the Event Horizon of the Black Hole. The regular nature of the Kruskal derivative is in sharp contrast with the Schwarzschild derivative, , at the Event Horizon. We also explicitly obtain the value of the Kruskal coordinates on the Event Horizon as a function of the constant of motion for a test particle on a radial geodesic. The physical implications of this result will be discussed elsewhere.