Schwarzschild Geodesics in Terms of Elliptic Functions and the Related Red Shift ()
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.
Share and Cite:
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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