On Some Classical and Quantum Effects Due to Gravitational Fields

We consider the gravitational fields generated by a cosmic string, a global monopole and a tubular matter with interior magnetic field (Safko-Witten space-time), and examine some classical and quantum effects due to these fields. We investigate the Aharonov-Bohm effect in the space-time of a cosmic string, using the loop variables. In the space-time of a global monopole, we calculate the total energy radiated by a uniformly moving charged scalar particle, for small solid angle deficit. We show that the radiated energy is proportional to the cube of the velocity of the particle and to the cube of the Lorenz factor, in the non-relativistic and ultra-relativistic cases, respectively. In the Safko-Witten space-time, we investigate the existence of an electrostatic self-force on a charged particle. We also consider a hydrogen atom in the background space-time generated by a cosmic string and we find the solutions of the corresponding Dirac equation and we determine the energy levels of the atom. We investigate how the topological features of this space-time lead to shifts in the energy levels as compared with the flat Minkowski space-time. We study the behavior of non-relativistic quantum particles interacting with a Kratzer potential in the space-time generated by a global monopole and we find the energy spectrum in the presence of this topological defect. In the Safko-Witten space-time, an investigation is also made concerning the interaction of an harmonic oscillator with this background gravitational field.