Are photons traveling down into a potential (i.e. gravitational) energy well blue shifted, and ones traveling out red shifted? In other words, can a photon posses gravitational potential? If so why doesnt a derivation of the Schwarzschild radius using the concept of photon energetics yield the same expression?

given: E = hf, E = mc^2, Ep = -GMm/r

m = Ec^-2 = hf/c^2

hf = GM(hf)/(r * c^2)

1 = GM/(r * c^2)

r = GM/c^2

Rsch = 2GM/c^2

Isn't Rsch the radius of the body?