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.

arXiv comment20 pages, no figure, computational error corrected, new material added

References in corpus (1)

• An analytic solution for weak-field Schwarzschild geodesics

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