Abstract
We deduce a new formula for the perihelion advance 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 with positive constants depending on the angular momentum of the test particle. It is especially useful for orbits with large eccentricities showing that as .
- Received 17 April 2011
DOI:https://doi.org/10.1103/PhysRevD.83.124010
© 2011 American Physical Society