Approximate analytical calculations of photon geodesics in the Schwarzschild metric

Understand

We develop a method for deriving approximate analytical formulae to integrate photon geodesics in a Schwarzschild spacetime.

• Based on this, we derive the approximate equations for light bending and propagation delay that have been introduced empirically.
• We then derive for the first time an approximate analytical equation for the solid angle.
• We discuss the accuracy and range of applicability of the new equations and present a few simple applications of them to known astrophysical problems.