TY  - JOUR
A1  - Schmidt, Hans-Jürgen
T1  - Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole
N2  - We deduce a new formula for the perihelion advance $Theta$ 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. The resulting formula has the structure $Theta = c_1 - c_2 ln(c^2_3 - 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 $Theta 	o infty$ as $e 	o c_3$.
Y1  - 2011
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/32433
UR  - http://link.aps.org/doi/10.1103/PhysRevD.83.124010
SN  - 1550-7998
ER  -