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

Gunter Scharf

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DOI: 10.4236/jmp.2011.24036                

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.

Keywords

Schwarzschild Geodesics, Red Shift

Conflicts of Interest

The authors declare no conflicts of interest.

References

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