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 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 $e o c_3$.
Author details: | Hans-Jürgen Schmidt |
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URL: | http://link.aps.org/doi/10.1103/PhysRevD.83.124010 |
ISSN: | 1550-7998 |
Publication type: | Article |
Language: | English |
Year of first publication: | 2011 |
Publication year: | 2011 |
Release date: | 2017/03/25 |
Source: | Physical Review D. - ISSN 1550-7998. - 83 (2011), 12, 124010 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |