Geusa De A. Marques

Hydrogen atom in the gravitational fields of topological defects

We consider a hydrogen atom in the background spacetimes generated by an infinitely thin cosmic string and by a pointlike global monopole. In both cases, we find the solutions of the corresponding Dirac equations and we determine the energy levels of the atom. We investigate how the geometric and topological features of these spacetimes lead to shifts in the energy levels as compared with the flat Minkowski spacetime.

Non-relativistic quantum systems on topological defects spacetimes

We study the behaviour of non-relativistic quantum particles interacting with different potentials in the spacetimes generated by a cosmic string and a global monopole. We find the energy spectra in the presence of these topological defects and show how they differ from their free-spacetime values.

QUANTUM EFFECTS DUE TO A MAGNETIC FLUX ASSOCIATED TO A TOPOLOGICAL DEFECT

We investigate the quantum scattering of an electron by a topological defect called dispiration, with an externally applied magnetic field along its axis. The Aharonov–Bohm effect for bound states is analyzed and it is demonstrated that the wave function and the energy spectra associated with the particle depend on the features of the dispiration as well as on the magnetic flux. We also calculate Berrys phase associated to the dynamics of electrons in this background.

SOLUTION OF THE DIRAC EQUATION WITH POSITION-DEPENDENT MASS IN A COULOMB AND SCALAR FIELDS IN A CONICAL SPACETIME

We consider the problem of a relativistic particle with position-dependent mass in the presence of a Coulomb and a scalar potentials in the background spacetime generated by a cosmic string. The scalar potential arises from the self-interaction potential which is induced by the conical geometry of the spacetime under consideration. We find the solution of the corresponding Dirac equation and determine the energy spectrum of the particle. The behavior of the energy levels on the parameters associated with the presence of the cosmic string and with the fact that the mass of the particle depends on its position is also analyzed.

SOME REMARKS ON THE GRAVITATIONAL AHARONOV–BOHM EFFECT

A massless spinor particle is considered in the background spacetimes generated by a moving mass current and by a spinning cosmic string. In the weak field approximation it is shown that the solution of the Weyl equations depends on the velocity of the source, which does not affect the curvature in this approximation in the case of a moving mass current. In the case of a spinning cosmic string, the solution of the Weyl equations depends on the deficit angle and on the angular momentum of the string. These effects may be viewed as examples of the gravitational analogues of the Aharonov–Bohm effect in electrodynamics.

REMARKS ON SOME QUANTUM EFFECTS IN A GLOBAL MONOPOLE SPACE–TIME

We study the behaviour of a nonrelativistic quantum particle interacting with the Kratzer molecular potential in the space–time of a global monopole. We find the energy spectrum and derive the scattering amplitude of massive particles propagating in these fields and show how they differ from their free-space values.

Spinor particles in the spacetimes of vacuumless defects

We obtain approximate solutions of the Dirac equation in the gravitational fields of vacuumless defects. In all obtained solutions we show the role played by the presence of these defects.

ON A RESULT CONCERNING THE BEHAVIOR OF A RELATIVISTIC QUANTUM SYSTEM IN THE COSMIC STRING SPACETIME

We consider the problem of a relativistic electron in the presence of a Coulomb potential and a magnetic field in the background spacetime corresponding to a cosmic string. We find the solution of the corresponding Dirac equation and determine the energy spectrum of the particle.

SOME REMARKS ON TOPOLOGICAL DEFECTS AND THEIR GRAVITATIONAL CONSEQUENCES

We calculate the energy radiated by a uniformly moving charged scalar particle in the spacetime of a point-like global monopole, for small solid angle deficit. We show that this 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. We also determine the energy shifts of a hydrogen atom placed in the background spacetime of a cosmic string and we discuss the possibility that these shifts could provide a means of probing for the presence of this topological defect in the Universe.