A Qualitative Study of the Complete Set of Solutions of the Differential Equation of Motion of a Test Particle in the Equatorial Plane of the Kerr Gravitational Field

摘要

A study is made of the mathematical solution of the differential equation of motion of a test particle in the equatorial plane of the Kerr gravitational field, using S (Schwarzschild-like) coordi-nates. A qualitative solution of this equation leads to the conclusion that there can only be 25 different types of orbits. For each value of a, the results are presented in a master diagram for which h and e are the parameters. A master diagram divides the h, e parameter space into regions such that at each point within one of these regions the types of admissible orbits are qualitatively the same. A pictorial representation of the physical orbits in the r, phi plane is also given. (Author)