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).
Author details: | Hans-Jürgen Schmidt |
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DOI: | https://doi.org/10.1103/PhysRevD.83.124010 |
ISSN: | 1550-7998 |
Title of parent work (English): | Physical review : D, Particles, fields, gravitation, and cosmology |
Publisher: | American Physical Society |
Place of publishing: | College Park |
Publication type: | Article |
Language: | English |
Year of first publication: | 2011 |
Publication year: | 2011 |
Release date: | 2017/03/26 |
Volume: | 83 |
Issue: | 12 |
Number of pages: | 9 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |