Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole
- We deduce a new formula for the perihelion advance Theta of a test particle in the Schwarzschild black hole by applying a newly developed nonlinear 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. The resulting formula has the structure Theta = c(1) - c(2) ln(c(3)(2) - e(2)) with positive constants c(1,2,3) depending on the angular momentum of the test particle. It is especially useful for orbits with large eccentricities e < c(3) < 1 showing that Theta -> infinity as e -> c(3).
