arXiv subjects

E. R. Bezerra de Mello

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

At least 91 records · Page 5Linked to original sources

arXiv2012

Casimir-Polder interaction between an atom and a conducting wall in cosmic string spacetime

The Casimir-Polder interaction potential is evaluated for a polarizable microparticle and a conducting wall in the geometry of a cosmic string perpendicular to the wall. The general case of the anisotropic polarizability tensor for the microparticle is considered. The corresponding force is a function of the wall-microparticle and cosmic string-microparticle distances. Depending on the orientation of the polarizability tensor principal axes the force can be either attractive or repulsive. The asymptotic behavior of the Casimir-Polder potential is investigated at large and small separations compared to the wavelength of the dominant atomic transitions. We show that the conical defect may be used to control the strength and the sign of the Casimir-Polder force.

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arXiv2012

Scalar self-energy for a charged particle in global monopole spacetime with a spherical boundary

We analyze combined effects of the geometry produced by global monopole and a concentric spherical boundary on the self-energy of a point-like scalar charged test particle at rest. We assume that the boundary is outside the monopole's core with a general spherically symmetric inner structure. An important quantity to this analysis is the three-dimensional Green function associated with this system. For both Dirichlet and Neumann boundary conditions obeyed by the scalar field on the sphere, the Green function presents a structure that contains contributions due to the background geometry of the spacetime and the boundary. Consequently the corresponding induced scalar self-energy present also similar structure. For points near the sphere the boundary-induced part dominates and the self-force is repulsive/attractive with respect to the boundary for Dirichlet/Neumann boundary condition. In the region outside the sphere at large distances from it, the boundary-free part in the self-energy dominates and the corresponding self-force can be either attractive or repulsive with dependence of the curvature coupling parameter for scalar field. In particular, for the minimal coupling we show the presence of a stable equilibrium point for Dirichlet boundary condition. In the region inside the sphere the nature of the self-force depends on the specific model for the monopole's core. As illustrations of the general procedure adopted we shall consider two distinct models, namely flower-pot and the ballpoint-pen ones.

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arXiv2012

Induced self-interactions in the spacetime of a global monopole with finite core

In this paper we analyze induced self-interactions for point-like particles with electric and scalar charges 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 the physical system under consideration. As we shall see for the charged particle outside the monopole core, the corresponding Green functions are composed by two distinct contributions, the firsts ones are induced by the non-trivial topology of the global monopole considered as a point-like defect and the seconds are corrections induced by the non-vanishing inner structure attributed to it. For both cases, the self-energies present a similar structure, having also two distinct contributions as well. For a specific model considered for region inside the monopole, named flower-pot, we shall see that the particle with electric charge will be always subject to a repulsive self-force with respect to the monopole core's boundary, on the other scalar charged particle exhibits peculiar behavior. Depending on the curvature coupling the self-force can be repulsive or attractive with respect to the core's boundary. Moreover, the contribution due to the point-like global monopole vanishes for massless particle conformally coupled with three dimensional space section of the manifold, and the only contribution comes from the core-induced part.

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arXiv2012

Fermionic Casimir densities in a conical space with a circular boundary and magnetic flux

The vacuum expectation value (VEV) of the energy-momentum tensor for a massive fermionic field is investigated in a (2+1)-dimensional conical spacetime in the presence of a circular boundary and an infinitely thin magnetic flux located at the cone apex. The MIT bag boundary condition is assumed on the circle. At the cone apex we consider a special case of boundary conditions for irregular modes, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The presence of the magnetic flux leads to the Aharonov-Bohm-like effect on the VEV of the energy-momentum tensor. For both exterior and interior regions, the VEV is decomposed into boundary-free and boundary-induced parts. Both these parts are even periodic functions of the magnetic flux with the period equal to the flux quantum. The boundary-free part in the radial stress is equal to the energy density. Near the circle, the boundary-induced part in the VEV dominates and for a massless field the vacuum energy density is negative inside the circle and positive in the exterior region. Various special cases are considered.

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arXiv2012

Vacuum polarization induced by a cosmic string in anti-de Sitter spacetime

In this paper we investigate the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor associated with a massive scalar quantum field induced by a generalized cosmic string in D-dimensional anti-de Sitter (AdS) spacetime. In order to develop this analysis we evaluate the corresponding Wightman function. As we shall observe, this function is expressed as the sum of two terms: the first one corresponds to the Wightman function in pure AdS bulk and the second one is induced by the presence of the string. The second contribution is finite at coincidence limit and is used to provide closed expressions for the parts in the VEVs of the field squared and the energy-momentum tensor induced by the presence of the string. Because the analysis of vacuum polarizations effects in pure AdS spacetime have been developed in the literature, here we are mainly interested in the investigation of string-induced effects. We show that the curvature of the background spacetime has an essential influence on the VEVs at distances larger than the curvature radius. In particular, at large distances the decay of the string-induced VEVs is power-law for both massless and massive fields. The string-induced parts vanish on the AdS boundary and they dominate the pure AdS part for points near the AdS horizon.

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arXiv2012

Topological Casimir effect in compactified cosmic string spacetime

We investigate the Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor for a massive scalar field with general curvature coupling in the generalized cosmic string geometry with a compact dimension along its axis. The boundary condition along the compactified dimension is taken in general form with an arbitrary phase. The vacuum expectation values are decomposed into two parts. The first one corresponds to the uncompactified cosmic string geometry and the second one is the correction induced by the compactification. The asymptotic behavior of the vacuum expectation values of the field squared, energy density and stresses are investigated near the string and at large distances. We show that the nontrivial topology due to the cosmic string enhances the vacuum polarization effects induced by the compactness of spatial dimension for both the field squared and the vacuum energy density. A simple formula is given for the part of the integrated topological Casimir energy induced by the planar angle deficit. The results are generalized for a charged scalar field in the presence of a constant gauge field. In this case, the vacuum expectation values are periodic functions of the component of the vector potential along the compact dimension.

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arXiv2011

Casimir effect for parallel metallic plates in cosmic string spacetime

We evaluate the renormalized vacuum expectation values (VEVs) of electric and magnetic fields squared and the energy-momentum tensor for the electromagnetic field in the geometry of two parallel conducting plates on background of cosmic string spacetime. On the base of these results, the Casimir-Polder force on a polarizable particle and the Casimir forces acting on the plates are investigated. The VEVs are decomposed into the pure string and plate-induced parts. The VEV of the electric field squared is negative for points with radial distance to the string smaller than the distance to the plates and positive for the opposite situation. On the other hand the VEV for the magnetic field squared is negative everywhere. The boundary induced part in the VEV of the energy-momentum tensor is different from zero in the region between the plates only. Moreover, this part only depends on the distance from the string. The boundary-induced part in the vacuum energy density is positive for points with distance to the string smaller than the distance to the plates and negative in opposite situation. The Casimir stresses on the plates depend non-monotonically on the distance from the string. We show that the Casimir forces acting on the plates are always attractive.

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arXiv2011

Gravitational Field of a Global Monopole in a Modified Gravity

In this paper we analyze the gravitational field of a global monopole in the context of $f(R)$ gravity. More precisely, we show that the field equations obtained are expressed in terms of $F(R)=\frac{df(R)}{dR}$. Since we are dealing with a spherically symmetric system, we assume that $F(R)$ is a function of the radial coordinate only. Moreover, adopting the weak field approximation, we can provide all components of the metric tensor. A comparison with the corresponding results obtained in General Relativity and in the Brans-Dicke theory is also made.

gr-qc↗

arXiv2011

Exact Casimir-Polder potential between a particle and an ideal metal cylindrical shell and the proximity force approximation

We derive the exact Casimir-Polder potential for a polarizable microparticle inside an ideal metal cylindrical shell using the Green function method. The exact Casimir-Polder potential for a particle outside a shell, obtained recently by using the Hamiltonian approach, is rederived and confirmed. The exact quantum field theoretical result is compared with that obtained using the proximity force approximation and a very good agreement is demonstrated at separations below 0.1$R$, where $R$ is the radius of the cylinder. The developed methods are applicable in the theory of topological defects.

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arXiv2011

Vacuum polarization by a flat boundary in cosmic string spacetime

In this paper we analyze the vacuum expectation values of the field squared and the energy-momentum tensor associated to a massive scalar field in a higher dimensional cosmic string spacetime, obeying Dirichlet or Neumann boundary conditions on the surface orthogonal to the string. In order to develop this analysis the corresponding Green function is obtained. The Green function is given by the sum of two expressions: the first one corresponds to the standard Green function in the boundary-free cosmic string spacetime and the second contribution is induced by the boundary. The boundary induced parts have opposite signs for Dirichlet and Neumann scalars. Because the analysis of vacuum polarization effects in the boundary-free cosmic string spacetime have been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions is investigated. We show that the non-trivial topology due to the cosmic string enhances the boundary induced vacuum polarization effects for both field squared and the energy-momentum tensor, compared to the case of a boundary in Minkowski spacetime. The presence of the cosmic string induces non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is investigated.

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arXiv2011

Induced self-energy on a static scalar charged particle in the spacetime of a global monopole with finite core

We analyze the induced self-energy and self-force on a scalar point-like charged test 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 scalar self-energy presents two distinct contributions. The first one is induced by the non-trivial topology of the global monopole considered as a point-like defect and the second is a correction induced by the non-vanishing inner structure attributed to it. For points inside the monopole, the self-energy also present a similar structure, where now the first contribution depends on the geometry of the spacetime inside. As illustrations of the general procedure adopted, two specific models, namely flower-pot and the ballpoint-pen, are considered for the region inside. For these two different situations, we were able to obtain exact expressions for the self-energies and self-forces in the regions outside and inside the global monopole.

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arXiv2011

Fermionic condensate in a conical space with a circular boundary and magnetic flux

The fermionic condensate is investigated in a (2+1)-dimensional conical spacetime in the presence of a circular boundary and a magnetic flux. It is assumed that on the boundary the fermionic field obeys the MIT bag boundary condition. For irregular modes, we consider a special case of boundary conditions at the cone apex, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The fermionic condensate is a periodic function of the magnetic flux with the period equal to the flux quantum. For both exterior and interior regions, the fermionic condensate is decomposed into boundary-free and boundary-induced parts. Two integral representations are given for the boundary-free part for arbitrary values of the opening angle of the cone and magnetic flux. At distances from the boundary larger than the Compton wavelength of the fermion particle, the condensate decays exponentially with the decay rate depending on the opening angle of the cone. If the ratio of the magnetic flux to the flux quantum is not a half-integer number, for a massless field the boundary-free part in the fermionic condensate vanishes, whereas the boundary-induced part is negative. For half-integer values of the ratio of the magnetic flux to the flux quantum, the irregular mode gives non-zero contribution to the fermionic condensate in the boundary-free conical space.

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arXiv2010

Fermionic current densities induced by magnetic flux in a conical space with a circular boundary

We investigate the vacuum expectation value of the fermionic current induced by a magnetic flux in a (2+1)-dimensional conical spacetime in the presence of a circular boundary. On the boundary the fermionic field obeys MIT bag boundary condition. For irregular modes, a special case of boundary conditions at the cone apex is considered, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. We observe that the vacuum expectation values for both charge density and azimuthal current are periodic functions of the magnetic flux with the period equal to the flux quantum whereas the expectation value of the radial component vanishes. For both exterior and interior regions, the expectation values of the current are decomposed into boundary-free and boundary-induced parts. For a massless field the boundary-free part in the vacuum expectation value of the charge density vanishes, whereas the presence of the boundary induces nonzero charge density. Two integral representations are given for the boundary-free part in the case of a massive fermionic field for arbitrary values of the opening angle of the cone and magnetic flux. The behavior of the induced fermionic current is investigated in various asymptotic regions of the parameters. At distances from the boundary larger than the Compton wavelength of the fermion particle, the vacuum expectation values decay exponentially with the decay rate depending on the opening angle of the cone. We make a comparison with the results already known from the literature for some particular cases.

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arXiv2010

Fermionic vacuum polarization by a cosmic string in de Sitter spacetime

We investigate the fermionic condensate and the vacuum expectation value of the energy-momentum tensor for a massive spinor field in the geometry of a straight cosmic string on background of de Sitter spacetime. By using the Abel-Plana summation formula, we explicitly extract form the expectation values the contribution associated with purely de Sitter space, remaining the expectation values induced by the cosmic string. The latter presents information about de Sitter gravity as well. Because the investigation of the fermionic quantum fluctuations in de Sitter space have been investigated in literature, here we are mainly interested in the cosmic string-induced contributions. For a massless field, the fermionic condensate vanishes and the presence of the string does not break chiral symmetry of the massless theory. Unlike to the case of a scalar field, for a massive fermionic field the vacuum expectation value of the energy-momentum tensor is diagonal and the axial and radial stresses are equal to the energy density. At large distances from the string the behavior of the string-induced parts in the vacuum densities is damping oscillatory with the amplitude decaying as the inverse fourth power of the distance. This is in contrast to the case of flat spacetime, in which the string-induced vacuum densities for a massive field decay exponentially with distance from the string. In the limit of the large curvature radius of de Sitter space we recover the results for a cosmic string in flat spacetime.

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arXiv2010

Vacuum polarization of a massive scalar field in a wormhole spacetime

We calculate the vacuum average value of the field square and the stress-energy tensor of a massive scalar field, with non-minimal coupling $ξ$ to the curvature in the short-throat flat-space wormhole background. The obtained results are not suitable for an analytical analysis and for this reason we provide a numerical analysis for different values of the coupling constant, $ξ$. It was shown that the vacuum polarization cannot self-consistently support the wormhole. Otherwise, the energy-momentum tensor does not violate the null energy condition near the throat.

gr-qc↗

arXiv2010

Induced fermionic current densities by magnetic flux in higher dimensional cosmic string spacetime

In this paper we analyse the vacuum fluctuations of quantum fermionic current densities, $ $, induced by a magnetic flux running along the core of the conical space produced by the presence of cosmic string, in a $(1+d)-$dimensional bulk, for $2\leq d\leq 5$. In order to develop this investigation we construct an expression for the fermionic propagator, which can be applied for those different dimensions of the spacetime. Two specific analysis for the induced current densities are presented: $(i)$ for massless fields in three and four dimensions, and $(ii)$ for massive fields in all dimensions considered. In the latter specific values for 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 are considered. Although being a very special situation and somewhat unnatural, the corresponding analysis of induced fermionic current densities under this circumstance may shed light on the qualitative behavior of these quantities in a more general situation.

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arXiv2010

Vacuum polarization by topological defects in de Sitter spacetime

In this paper we investigate the vacuum polarization effects associated with a massive quantum scalar field in de Sitter spacetime in the presence of gravitational topological defects. Specifically we calculate the vacuum expectation value of the field square, $<Φ^2>$. 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 defects.

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arXiv2010

Vacuum polarization by a scalar field in de Sitter spacetime in the presence of global monopole

In this paper we analyse the vacuum polarization effects associated with massive scalar quantum fields in a higher-dimensional de Sitter space in the presence of a global monopole. Because this analysis has been developed in a pure de Sitter space, here we are mainly interested on the effects induced by the presence of the global monopole. So, in order to achieve this objective we calculate the corresponding Wightman function, which is expressed in an integral representation and explicitly depends on the parameters associated with the presence of the monopole and the cosmological constant. Admitting that the former is closed to the unity, which corresponds to a realistic value predicted by Grand Unified Theories, it is possible to express this function as the sum of two terms: the first one corresponds to the Wightman function on the bulk where the global monopole is absent, and the second one is a contribution induced by the presence of the monopole.

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