Geodesics of Schwarzschild

In section 5.4 Carroll explores the geodesics of Schwarzschild. These turn out to be almost useless as far as I can see. What are very useful are the Killing vector fields in Schwarzschild. In particular the energy Killing vector field which will eventually enable us to find an equation fro the path of a radially free-falling test particle. I learnt why Killing vectors are so important!

In this section we also write out the useless geodesic equations and work out some potentials. Most of it is pretty dry stuff. So dry that I forgot to post it until I actually used the equations with some success in late June.

All at Commentary 5.4 Geodesics of Schwarzschild.pdf