Neutral particle trajectory in the Kerr field

• Published in: Journal of astrophysics and astronomy Vol. 40; no. 6; pp. 1 - 12
• Main Authors: Haque, Enamul, Bhuyan, M. D. I.
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.12.2019; Springer Nature B.V
• Subjects: Angular momentum; Astronomy; Astrophysics and Astroparticles; Coordinates; Differential equations; Eccentric orbits; Equations of motion; Motion stability; Neutral particles; Observations and Techniques; Orbital stability; Particle trajectories; Perturbation methods; Physics; Physics and Astronomy; Power series; Rotation; Kerr metric; Lindiquist coordinates; isotropic coordinates; Lindstedt and Poincaré method; perihelion advance; Boyer
• ISSN: 0250-6335; 0973-7758
• DOI: 10.1007/s12036-019-9611-4

In this paper, the neutral particle trajectory around a rotating black hole in the four-dimensional Kerr space–time is studied. The equation of motion is derived by using the Kerr metric within the slowly rotating and weak-field limit. The stability conditions of the orbital motion of the neutral particle are deduced. For small amplitude of motion, the approximate solutions of the resulting differential equations are obtained by the perturbation method of Lindstedt and Poincaré. These are then expressed as power series for some small perturbation parameters. The angular frequencies are also found in the corresponding order of the perturbation. By using angular frequencies, an expression of the perihelion advance is derived. To find the orbital equation similar to Newtonian orbit, the coordinate system is transformed into isotropic coordinates. The Newtonian orbital equation is derived and hence the eccentricity of the orbit is obtained. The resulting expression of circular motion shows the relationship between energy and angular momentum of a spinning particle in the Kerr field.