The reverse passage takes spacetime geodesics for a nonrotating black hole in the equatorial plane (a 3-d spacetime) to motion under a central "gravitational force field". The conformal transformation to the optical metric converts the solutions to geodesics on the deformed equatorial plane (like the Jacobi reparametrization). The embedding diagrams then show the reversal of centrifugal force.
I think this explains ur problems ERU. A solution from here should be simple.