Schwarzschild geodesics in terms of elliptic functions and the related red shift

Understand

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.