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arXiv · 1101.1207

Schwarzschild geodesics in terms of elliptic functions and the related red shift

Gunter Scharf
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Abstract

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.

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Gunter Scharf. 2011-01-31. Schwarzschild geodesics in terms of elliptic functions and the related red shift. https://doi.org/10.4236/jmp.2011.24036

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