Schwarzschild Geodesics in Terms of Elliptic Functions and the Related Red Shift

• 作者: Gunter Scharf
• 来源期刊: 现代物理(英文)
• 学科: 数学
• 关键词: SCHWARZSCHILD GEODESICS RED SHIFT
• 年，卷（期）: 2011,（4）
• 页码范围: 274-283
• 页数: 10页
• 分类号: O1

摘要

Using Weierstrassian elliptic functions the exact geodesics in the Schwarzschild metric are expressed in a simple and most transparent form. The results are useful for analytical and numerical applications. For example we calculate the perihelion precession and the light deflection in the post-Einsteinian approximation. The bounded orbits are computed in the post-Newtonian order. As a topical application we calculate the gravitational red shift for a star moving in the Schwarzschild field.