Quote by Machinus
I stated in my post that the object has a mass m. Photons do not have mass. Light is not an appropriate example for this orbit.
The radial velocity reaches a maximum at some point between infinity and the minimum r. The fact that the velocity is all radial at infinity is irrelevant to finding the maximum [tex]\dot{r}[/tex].

the massive particle that is sent at the black hole at speed 0.999 c
will follow approximately the same trajectory as the photon
if you want to make the approximation better, send a new particle at
0.9999 c
and then one at 0.99999 c
the particles follow geodesics in spacetimethe spacetime created by the massive central body, the black hole. approximately the same paths as photons of light
if you think about it in an openminded fashion, I believe you will come to the conclusion that the maximum radial velocity (what you asked about in your question) is c.