Perihelion advance for orbits with large eccentricities in the   Schwarzschild black hole
  We deduce a new formula for the perihelion advance of a test particle in the Schwarzschild black hole by applying a newly developed non-linear transformation within the Schwarzschild space-time. By this transformation we are able to apply the well-known formula valid in the weak-field approximation near infinity also to trajectories in the strong-field regime near the horizon of the black hole. 
H.-J. Schmidt
gr-qc astro-ph.CO