Geusa de A. Marques

Scalar solutions in spacetimes containing a cosmic string

Scalar quantum particles are considered in the Kerr–Newman, Godel and Friedmann–Robertson–Walker spacetimes with a cosmic string passing through them. The solutions of the Klein–Gordon equation in these backgrounds are obtained and some of their consequences are discussed, with emphasis on the role played by the presence of the cosmic string.

Some effects on quantum systems due to the gravitational field of a cosmic string

We study the behavior of a nonrelativistic quantum particle interacting with different potentials in the background space-time generated by a cosmic string. We find the energy spectra for the quantum systems under consideration and discuss how they differ from their flat Minkowski space-time values.

Comment to: “Corrections to the fine structure constant in the spacetime of a cosmic string from the generalized uncertainty principle” [Phys. Lett. B 632 (2006) 151]

Abstract In the paper [F. Nasseri, Phys. Lett. B 632 (2006) 151–154], F. Nasseri supposed that the value of the angular momentum for the Bohrs atom in the presence of the cosmic string is quantized in units of ℏ . Using this assumption it was obtained an incorrect expression for Bohr radius in this scenario. In this Comment I want to point out that this assumption is not correct and present a corrected expression for the Bohr radius in this background.

On a class of solutions of the Einstein–Maxwell field equations in scalar-tensor theories of gravity

In this paper we obtain a class of static cylindrically symmetric solutions of the Einstein–Maxwell field equations in the framework of scalar-tensor theories of gravity. In this context, in which both a Maxwell field and a dilaton field are sources of the stress energy, the solutions were obtained by using the Rainich conditions of general relativity, appropriately modified to take into account the presence of the scalar field.

Gravitational Aharonov-Bohm effect due to weak fields

We study the behavior of relativistic quantum particles in the space-times generated by a rotating massive body and a moving mass current, in the weak field approximation. We solve the Dirac equation in these gravitational fields and calculate the currents associated with the particles. It is shown that these solutions and the currents depend on the angular momentum and on the velocity of the sources, in the cases of a massive rotating body and a moving mass current, respectively. These effects may be looked upon as a gravitational analog of the Aharonov-Bohm effect.

Some effects on relativistic quantum systems due to a weak gravitational field

We study the behaviour of relativistic quantum particles in the space-time generated by a moving mass current, in the weak field approximation. We solve the Dirac equation in this gravitational field and calculate the current associated with the particles. The study of the behaviour of quantum systems under the influence of curved space-times goes back to the end of the 1920s and to the beginning of the 1930s[1], when the generalization of the Schr ¨ odinger and Dirac equations to curved spaces has been discussed, motivated by the idea of constructing a theory combining quantum physics and general relativity. Along this line of research the hydrogen atom has been studied in particular curved space-times[2, 3]. These investigations showed that the energy levels of an atom placed in a gravitational field is shifted as a result of the interaction of the atom with the space-time curvature[3]-[5]. This shift in the energy of each atomic level would depend on the features of the space-time. The general theory of relativity, as a metric theory, predicts that gravitation is manifested as the curvature of space-time. Therefore, it is of interest to know how the curvature of spacetime at the position of the atom affects its spectrum. On the other hand, we know that there are situations in which particles are constrained to move in a region where the Riemann curvature tensor vanishes and even in this case they exhibit gravitational effects arising from a region of non-zero curvature from which they are excluded[6]. In a more general sense, we have the case in which particles are constrained to move in a region where the Riemann curvature tensor does not vanish but does depend on certain parameter of the metric such as the velocity or the angular momentum of the source. In this case we have effects on the system associated with parameters which do not influence the curvature of the space-time as we will see. In what follows we present the study concerning the behaviour of a relativistic particle placed in the gravitational field generated by a cylindrical distribution of matter with uniform density along the z-axis moving slowly, whose metric reads[7]

CORRECTIONS TO THE FINE STRUCTURE CONSTANT IN (D+1)-DIMENSIONAL GLOBAL MONOPOLE SPACETIME

In this paper we use the Generalized Uncertainty Principle in order to obtain the corrections to the fine structure constant in (D + 1)-dimensional global monopole spacetime. We also discuss the case D = 3 corresponding to the (3+1)-dimensional global monopole spacetime.

Some effects on quantum systems due to the gravitational field of a topological defect

We study the behavior of a non-relativistic quantum particle interacting with different potentials, in the background space-time generated by a cosmic string. We find the energy spectra for the quantum systems under consideration and discuss how they differ from their flat Minkowski space-time values.