The Motion Of Spinning Particles In Curved Spacetimes

In this paper we investigate the pseudo-classical spinning particles in curved spacetimes by pseudo-classical mechanics models in which the spin degrees of freedom are characterized in terms of anti-commuting Grassmann variables. Pseudo-classical spinning point particles are described by the supersymmetric extension of the usual relativistic particle. Now we known that the geometry of the graded pseudo-manifolds with both number and Grassmann coordinates has been found to be of wide mathematical interest,and the spacetime symmetries have close relations with the motion of spinning particles. So this research has the vital significance in the thorough discussion of the spacetime symmetries.In the first chapter ,we investigate the geodesic motion of a test particle in curved spacetimes with a perfect mathematical method.After calculations, we obtain some expressions of the orbital effect for a test particle and some meaningful results in different black hole spacetimes.By detailed analysis and comparion , we obtain the contributions of electric(or magnetic) charge,electric(or magnetic) moment and cosmological parameters to the perihelion precession.These theoretical results we given correspond to the results by experiment.In the second chapter ,the generalized Killing equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. We study the geodesic motion of pseudo-classical spinning particles both in stationary symmetric and axisymmetric spacetimes. We discuss the special cases of motion in a plane.Becase of the angular momentum per unit mass,the spinning particles in Kerr spactime are different from those in stationary symmetric spacetimes,and we obtain some expressions in detail.Finally ,we study the equilibrium of a spinning particle in Reissner-Nordstr(o|¨)m-(anti-)de Sitter spacetime and Kerr spacetime.We found that equilibrium conditions are independent of the spin of the test particles in Reissner-Nordstrom spacetime due to the spherical symmetry of the spacetimes.But the equilibrium in Kerr spacetime is possible only on the equatorial plane and the rotation axis and nowwhere else,owing to the rotation inherent to the spacetime.