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

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DOI: 10.4236/jmp.2011.24036    4,898 Downloads   9,228 Views   Citations
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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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

References

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