arXiv subjects

E. R. Bezerra de Mello

Publications and source records attributed to E. R. Bezerra de Mello.

At least 109 records · Page 6Linked to original sources

arXiv2009

Spherically symmetric vacuum solutions of modified gravity theory in higher dimensions

In 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 $F(R)=\frac{df(R)}{dR}$. 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.

gr-qc↗

arXiv2009

Vacuum polarization by a cosmic string in de Sitter spacetime

In this paper we investigate the vacuum polarization effect associated with a quantum massive scalar field in a higher dimensional de Sitter spacetime in the presence of a cosmic string. Because this investigation has been developed in a pure de Sitter space, here we are mainly interested on the effects induced by the presence of the string. So this analysis is developed by expressing the complete Wightman function as the sum of two terms: The first one corresponds to the bulk where the cosmic string is absent and the second one is induced by the presence of the string. By using the Abel-Plana summation formula, we show that for points away from the string the latter is finite at the coincidence limit and it is used to evaluate the vacuum averages of the square of the field and the energy-momentum tensor induced by the cosmic string. Simple asymptotic formulae are obtained for these expectation values for points near the string and at large distances from it. It is shown that, depending on the curvature radius of de Sitter spacetime, two regimes are realized with monotonic and oscillatory behavior of the vacuum expectation values at large distances.

hep-th↗

arXiv2008

Fermionic vacuum densities in higher-dimensional de Sitter spacetime

Fermionic condensate and the vacuum expectation values of the energy-momentum tensor are investigated for twisted and untwisted massive spinor fields in higher-dimensional de Sitter spacetime with toroidally compactified spatial dimensions. The expectation values are presented in the form of the sum of corresponding quantities in the uncompactified de Sitter spacetime and the parts induced by non-trivial topology. The latter are finite and the renormalization is needed for the first parts only. Closed formulae are derived for the renormalized fermionic vacuum densities in uncompactified odd-dimensional de Sitter spacetimes. It is shown that, unlike to the case of 4-dimensional spacetime, for large values of the mass, these densities are suppressed exponentially. Asymptotic behavior of the topological parts in the expectation values is investigated in the early and late stages of the cosmological expansion. When the comoving lengths of compactified dimensions are much smaller than the de Sitter curvature radius, to the leading order the topological parts coincide with the corresponding quantities for a massless fermionic field and are conformally related to the corresponding flat spacetime results. In this limit the topological parts dominate the uncompactified de Sitter part and the back-reaction effects should be taken into account. In the opposite limit, for a massive field the asymptotic behavior of the topological parts is damping oscillatory.

hep-th↗

arXiv2008

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

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.

hep-th↗

arXiv2008

Vacuum polarization by fermionic fields in higher dimensional cosmic string space-time

In this paper we investigate vacuum polarization effects associated with charged massive quantum fermionic fields in a six-dimensional cosmic string space-times considering the presence of a magnetic flux running along its core. We have shown that for specific values of the parameters which codify the presence of the cosmic string, and the fractional part of the ratio of the magnetic flux by the quantum one, a closed expression for the respective Green function is obtained. Adopting this result, we explicitly calculate the renormalized vacuum expectation value of the energy-momentum tensors, $ _{Ren}$, and analyse this result in some limitting cases.

hep-th↗

arXiv2008

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

In this paper we investigate the vacuum polarization effects associated with quantum fermionic charged fields in a generalized $(d+1)-$dimensional cosmic string space-times considering the presence of a magnetic flux along the string. In order to develop this analysis we calculate a general expression for the respective Green function, valid for several different values of $d$, which is expressed in terms of a bispinor associated with the square of the Dirac operator. Adopting this result, we explicitly calculate the renormalized vacuum expectation values of the energy-momentum tensors, $ _{Ren.}$, associated with massless fields. Moreover, for specific values of the parameters which codify the cosmic string and the fractional part of the ratio of the magnetic flux by the quantum one, we were able to present in closed forms the bispinor and the respective Green function for massive fields.

hep-th↗

arXiv2008

Induced electrostatic self-interaction in the spacetime of a global monopole with inner structure

In this work we analise the electrostatic self-energy and self-force on a point-like electric charged particle induced by a global monopole spacetime considering a inner structure to it. In order to develop this analysis we calculate the three-dimensional Green function associated with this physical system. We explicitly show that for points inside and outside the monopole's core the self-energy presents two distinct contributions. The first is induced by the geometry associated with the spacetime under consideration, and the second one is a correction due to the non-vanishing inner structure attributed to it. Considering specifically the ballpoint-pen model for the region inside, we were able to obtain exact expressions for the self-energies in the regions outside and inside the monopole's core.

hep-th↗

arXiv2008

Fermionic vacuum polarization by a composite topological defect in higher-dimensional space-time

We investigate the vacuum polarization effects associated with a charged massless spin-1/2 field in a higher-dimensional space-time, induced by a composite topological defect. The defect is constituted by a global monopole living on a three-brane and two-dimensional conical space transverse to the latter. In addition, we assume the presence of an extra magnetic flux along the core of the conical space. The heat kernel and the Feynman Green function are presented in the form of a sum of two terms. The first one corresponds to the contribution coming from the bulk with global monopole in the absence of conical structure of the orthogonal two-space, and the second one is induced by this structure and the magnetic flux. We explicitly evaluate the part in the vacuum expectation value of the energy-momentum tensor induced by the flux carrying conical structure. As in pure cosmic string geometries, only the fractional part of the ratio of the magnetic flux to flux quantum leads to non-trivial effects. The vacuum energy-momentum tensor is an even function of this parameter. We show that for strong gravitational fields corresponding to large values of the solid angle deficit, the effects induced by the conical structure and flux are exponentially suppressed.

hep-th↗

arXiv2008

Vacuum Polarization by a Magnetic Flux Tube at Finite Temperature in the Cosmic String Spacetime

In this paper we analyse the effect produced by the temperature in the vacuum polarization associated with charged massless scalar field in the presence of magnetic flux tube in the cosmic string spacetime. Three different configurations of magnetic fields are taken into account: $(i)$ a homogeneous field inside the tube, $(ii)$ a field proportional to $1/r$ and $(iii)$ a cylindrical shell with $δ$-function. In these three cases, the axis of the infinitely long tube of radius $R$ coincides with the cosmic string. Because the complexity of this analysis in the region inside the tube, we consider the thermal effect in the region outside. In order to develop this analysis, we construct the thermal Green function associated with this system for the three above mentioned situations considering points in the region outside the tube. We explicitly calculate in the high-temperature limit, the thermal average of the field square and the energy-momentum tensor.

hep-th↗

arXiv2007

On Matrix Superpotential and Three-Component Normal Modes

We consider the supersymmetric quantum mechanics (SUSY QM) with three- component normal modes for the Bogomol'nyi-Prasad-Sommerfield (BPS) states. An explicit form of the SUSY QM matrix superpotential is presented and the corresponding three-component bosonic zero-mode eigenfunction is investigated.

hep-th↗

arXiv2007

Fermionic vacuum polarization in higher-dimensional global monopole spacetime

In this paper we analyse the vacuum polarization effects associated with a massless fermionic field in a higher-dimensional global monopole spacetime in the "braneworld" scenario. In this context we admit that the our Universe, the bulk, is represented by a flat $(n-1)-$dimensional brane having a global monopole in a extra transverse three dimensional submanifold. We explicitly calculate the renormalized vacuum average of the energy-momentum tensor, $ _{Ren.}$, admitting the global monopole as being a point-like object. We observe that this quantity depends crucially on the value of $n$, and we provide explicit expressions to it for specific values attributed to $n$.

hep-th↗

arXiv2007

Polarization of the fermionic vacuum by a global monopole with finite core

We study the vacuum polarization effects associated with a massive fermionic field in a spacetime produced by a global monopole considering a nontrivial inner structure for it. In the general case of the spherically symmetric static core with finite support we evaluate the vacuum expectation values of the energy-momentum tensor and the fermionic condensate in the region outside the core. These quantities are presented as the sum of point-like global monopole and core-induced contributions. The asymptotic behavior of the core-induced vacuum densities are investigated at large distances from the core, near the core and for small values of the solid angle corresponding to strong gravitational fields. As an application of general results the flower-pot model for the monopole's core is considered and the expectation values inside the core are evaluated.

hep-th↗

arXiv2006

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

hep-th↗

arXiv2006

Electrostatic self-interaction in the spacetime of a global monopole with finite core

In this paper we calculate the induced electrostatic self-energy and self-force for an electrically charged particle placed at rest in the spacetime of a global monopole admitting a general spherically symmetric inner structure to it. In order to develop this analysis we calculate the three-dimensional Green function associated with this physical system. We explicitly show that for points outside the monopole's core the self-energy presents two distinct contributions. The first is induced by the non-trivial topology of the global monopole considered as a point-like object. The second is a correction induced by the non-vanishing inner structure attributed to it. As an illustration of the general procedure the flower-pot model for the region inside the monopole is considered. In this application it is also possible to find the electrostatic self-energy for points in the region inside the monopole. In the geometry of the global monopole with the positive solid angle deficit, we show that for the flower-pot model the electrostatic self-force is repulsive with respect to the core surface for both exterior and interior regions.

hep-th↗

arXiv2006

SUSY QM from Three Domain Walls in a Scalar Potential

We investigate the linear classical stability of Bogomol'nyi-Prasad-Sommerfield (BPS) on three domain wall solutions in a system of three coupled real scalar fields, for a general positive potential with a square form. From a field theoretic superpotential evaluated on the domain states, the connection between the supersymmetric quantum mechanics involving three-component eigenfunctions and the stability equation associated with three classical configurations is elaborated.

hep-th↗

arXiv2006

Vacuum Polarization in the Presence of Magnetic Flux at Finite Temperature in the Cosmic String Background

In this paper we analyse the vacuum polarization effect associated with the charged massless scalar field, in the presence of magnetic flux at finite temperature, in the cosmic string background. We consider a spacetime of an idealized cosmic string which presents a magnetic field confined in a cylindrical tube of finite radius. Two different situations are taken into account in our analysis: (i) a homogeneous field inside the tube and (ii) a magnetic field proportional to $1/r$. In these two cases, the axis of the infinitely long tube of radius $R$ coincides with the cosmic string. Specifically, we calculate the effects produced by the temperature in the renormalized vacuum expectation value of the square of the charged massless scalar field, $<\hatϕ^{\ast}(x)\hatϕ(x)>$. Therefore, in order to realize these analysis, we calculate the Euclidean Green function associated with this field in this background.

hep-th↗

arXiv2006

Vacuum polarization by a global monopole with finite core

We investigate the effects of a $(D+1)$-dimensional global monopole core on the behavior of a quantum massive scalar field with general curvature coupling parameter. In the general case of the spherically symmetric static core, formulae are derived for the Wightman function, for the vacuum expectation values of the field square and the energy-momentum tensor in the exterior region. These expectation values are presented as the sum of point-like global monopole part and the core induced one. The asymptotic behavior of the core induced vacuum densities is investigated at large distances from the core, near the core and for small values of the solid angle corresponding to strong gravitational fields. In particular, in the latter case we show that the behavior of the vacuum densities is drastically different for minimally and non-minimally coupled fields. As an application of general results the flower-pot model for the monopole's core is considered and the expectation values inside the core are evaluated.

hep-th↗

arXiv2006

Vacuum Polarization Effects in Higher Dimensional Global Monopole Spacetime

In this paper we analyse the vacuum polarization effects associated with a massless scalar field in higher-dimensional global monopole spacetime. Specifically we calculate the renormalized vacuum expectation value of the field square, $<Φ^2(x)>_{Ren}$, induced by a global monopole. Two different spacetimes will be considered: $i)$ In the first, the global monopole lives in whole universe, and $ii)$ in the second, the global monopole lives in a $n=3$ dimensional sub-manifold of the higher-dimensional (bulk) spacetime in the "braneworld" scenario. In order to develop these analysis we calculate the general Euclidean scalar Green function for both spacetimes. Also a general curvature coupling parameter between the field and the geometry is admitted. We explicitly show that $<Φ^2(x)>_{Ren}$ depends crucially on the dimension of the spacetime and on the specific geometry adopted to describe the world. We also investigate the general structure of the renormalized vacuum expectation value of the energy-momentum tensor, $ _{Ren.}$.

hep-th↗