E. R. Bezerra de Mello

Landau levels in the presence of disclinations

Abstract This work is an investigation of the influence of a disclination on the spectrum of an electron or hole in a magnetic field in the framework of the theory of defects/three-dimensional gravity of Katanaev and Volovich. The presence of the defect reduces the degeneracy of the Landau levels to a finite value, except for very particular deficit angles. Inclusion of the self-interaction in the study further breaks the degeneracy. Exact wavefunctions and energy eigenvalues are found for special values of the magnetic field.

Relativistic quantum dynamics of a charged particle in cosmic string spacetime in the presence of magnetic field and scalar potential

In this paper we analyze the relativistic quantum motion of charged spin-0 and spin-\(\frac{1}{2}\) particles in the presence of a uniform magnetic field and scalar potentials in the cosmic string spacetime. In order to develop this analysis, we assume that the magnetic field is parallel to the string and the scalar potentials present a cylindrical symmetry with their center on the string. Two distinct configurations for the scalar potential, S(r), are considered: (i) the potential proportional to the inverse of the polar distance, i.e., S∝1/r, and (ii) the potential proportional to this distance, i.e., S∝r. The energy spectra are explicitly computed for different physical situations and their dependences on the magnetic field strength and scalar coupling constants are presented.

Vacuum polarization induced by a cylindrical boundary in the cosmic string spacetime

In this paper we investigate the Wightman function, the renormalized vacuum expectation values of the field square, and the energy-momentum tensor for a massive scalar field with general curvature coupling inside and outside of a cylindrical shell in the generalized spacetime of straight cosmic string. For the general case of Robin boundary condition, by using the generalized Abel-Plana formula, the vacuum expectation values are presented in the form of the sum of boundary-free and boundary-induced parts. The asymptotic behavior of the vacuum expectation values of the field square, energy density and stresses are investigated in various limiting cases. The generalization of the results to the exterior region is given for a general cylindrically symmetric static model of the string core with finite support.

Spherically symmetric vacuum solutions of modified gravity theory in higher dimensions

AbstractIn this paper we investigate spherically symmetric vacuum solutions of f(R) gravity in a higher-dimensional spacetime. With this objective we construct a system of non-linear differential equations whose solutions depend on the explicit form assumed for the function

Electromagnetic Casimir densities induced by a conducting cylindrical shell in the cosmic string spacetime

F(R)=\frac{df(R)}{dR}

Fermionic vacuum polarization by a cylindrical boundary in the cosmic string spacetime

. We explicit show that for specific classes of this function exact solutions from the field equations are obtained; also we find approximated results for the metric tensor for more general cases admitting F(R) close to the unity.

Vacuum polarization of a massless spinor field in global monopole spacetime

We investigate the renormalized vacuum expectation values of the field square and the energy-momentum tensor for the electromagnetic field inside and outside of a conducting cylindrical shell in the cosmic string spacetime. By using the generalized Abel-Plana formula, the vacuum expectation values are presented in the form of the sum of boundary-free and boundary-induced parts. The asymptotic behavior of the vacuum expectation values of the field square, energy density and stresses are investigated in various limiting cases.

Spinor Green function in higher-dimensional cosmic string space-time in the presence of magnetic flux

The vacuum expectation values of the energy-momentum tensor and the fermionic condensate are analyzed for a massive spinor field obeying the MIT bag boundary condition on a cylindrical shell in the cosmic string spacetime. Both regions inside and outside the shell are considered. By applying to the corresponding mode sums a variant of the generalized Abel-Plana formula, we explicitly extract the parts in the expectation values corresponding to the cosmic string geometry without boundaries. In this way the renormalization procedure is reduced to that for the boundary-free cosmic string spacetime. The parts induced by the cylindrical shell are presented in terms of integrals rapidly convergent for points away from the boundary. The behavior of the vacuum densities is investigated in various asymptotic regions of the parameters. In the limit of large values of the planar angle deficit, the boundary-induced expectation values are exponentially suppressed. As a special case, we discuss the fermionic vacuum densities for the cylindrical shell on the background of the Minkowski spacetime.

Exact solutions of the Klein–Gordon equation in the presence of a dyon, magnetic flux and scalar potential in the spacetime of gravitational defects

We calculate the renormalized vacuum average of the energy-momentum tensor of a massless left-handed spinor field in the pointlike global monopole spacetime using point-separation approach. The general structure of the vacuum average of the energy-momentum tensor is obtained and expressed in terms of a

Vacuum polarization by a flat boundary in cosmic string spacetime

〈{T}_{0}^{0}{〉}^{\mathrm{ren}}