Schwarzschild Geodesics in Terms of Elliptic Functions and the Related Red Shift
Gunter Scharf
DOI: 10.4236/jmp.2011.24036   PDF   HTML     5,231 Downloads   9,647 Views   Citations


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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G. Scharf, "Schwarzschild Geodesics in Terms of Elliptic Functions and the Related Red Shift," Journal of Modern Physics, Vol. 2 No. 4, 2011, pp. 274-283. doi: 10.4236/jmp.2011.24036.

Conflicts of Interest

The authors declare no conflicts of interest.


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