Neutral particle trajectory in the Kerr field

  • Enamul HaqueEmail author
  • M. D. I. Bhuyan


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.


Kerr metric Lindstedt and Poincaré method perihelion advance Boyer Lindiquist coordinates isotropic coordinates 


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Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of PhysicsMawlana Bhashani Science and Technology UniversitySantoshBangladesh

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