Higher-order geodesic deviations applied to the Kerr metric

Details Higher-order geodesic deviations applied to the Kerr metric Higher-order geodesic deviations applied to the Kerr metric

2002-05-06

arxiv.org/abs/gr-qc/0205019v1

Class.Quant.Grav. 19 (2002) 4573-4590

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, LaTeX

Scientific paper

10.1088/0264-9381/19/17/309

Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a General Relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this method to the problem of closed orbital motion of test particles in the Kerr metric space-time. With a simple circular orbit in the equatorial plane taken as the initial geodesic we obtain finite eccentricity orbits in the form of Taylor series with the eccentricity playing the role of small parameter. The explicit expressions of these higher-order geodesic deviations are derived using successive systems of linear equations with constant coefficients, whose solutions are of harmonic oscillator type. This scheme gives best results when applied to the orbits with low eccentricities, but with arbitrary values of $(GM/Rc^2)$, smaller than 1/6 in the Schwarzschild limit.

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