Also, could you please expand on how I could calculate the four-momentum using the geodesic equation? I believe that’s the method my professor would like me to use, as stated in the problem. Thank you.
Just so I’m clear, ##\frac{\partial L}{\partial \dot x_i}## means the partial of the lagrangian with respect to each coordinate right? So the four momentum has components in coordinates {t, r, ##\theta##, ##\phi##}, so those components are found by finding ##\frac{\partial L}{\partial \dot t}##...
I have calculated the Christoffel symbols for the above given metric, but I don't understand how to calculate a photon's four-momentum using this information. I believe it has something to do with the null geodesic equation but I can't understand how to put that information into the problem...