Stability of Spinning Objects in the Kerr-Newman Field

Abstract

This thesis presents a study of the motion of objects in the Kerr- Newman field and its special cases, namely the Reissner-Nordström field and the Kerr field. The motion of four types of objects is investigated: neutral or charged objects, and spin-less or spinning objects (an object as it rotates around an axis through its center of mass). For each type, the features of the orbital motion are explored, and the conditions for stability are derived. The thesis consists of four chapters as follows: Chapter I: briefly reviews the geometric structure and the Riemannian geometry, in which the field equations are described in general relativity theory. In addition, geodesic equations, equations of motion of a spinning test particle, equations of motion of a charged test particle, and equations of motion of a spinning charged test particle are all addressed in this chapter. Chapter II: examines the perihelion advance and the stability criterion of a spinning charged test particle in the Reissner-Nordström field, and applies them to the Earth orbit. In the present chapter, an equation of motion of a spinning charged test particle is examined, which is the counterpart of Papapetrou equations in Riemannian geometry when the charge of the particle disappears. By using the Lagrangian approach, the equation of motion of the spinning charged particle is derived. Furthermore, the path deviation of the spinning charged particle is achieved by the same Lagrangian function. The equation of motion of the spinning charged test particle, in the Reissner-Nordström background, is entirely solved. The stability criteria of the spinning motion of the charge test particle are discussed. The Perihelion advance and trajectory of a spinning charged test particle, in the Reissner-Nordström space-time, are scrutinized with two different methods; namely, the perturbation method (Einstein’s method) and that described by (Kerner et al., 2000), respectively. Moreover, the effects of charge and spin on Perihelion advance are inspected. Additionally, the existing results correspond to the previously cited works. Finally, applications to the Earth's orbit are also analyzed.