Vacuum polarization by a global monopole with finite core

Mello, E. R. Bezerra de; Saharian, A. A.

doi:10.1088/1126-6708/2006/10/049

Cited by 16 publications

(11 citation statements)

References 22 publications

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“…This spacetime corresponds to Minkowski one which can be easily verified by expressing the above line element in terms of the new radial coordinate, r = r + (α − 1)a. As we have mentioned before, from the Israel matching conditions for the metric tensors corresponding to (1.1) and (4.1), we find the singular contribution for the Ricci curvature located on the core's surface r = a [19]:…”

Section: Flower-pot Modelsupporting

confidence: 57%

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

Mello¹,

Saharian²

2012

Class. Quantum Grav.

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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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Section: Flower-pot Modelsupporting

confidence: 57%

“…The analysis of vacuum polarization effect associated with scalar and fermionic fields, considering the flower-pot model for the region inside the monopole, has been developed in[19] and[20], respectively.…”

mentioning

confidence: 99%

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

Mello¹,

Saharian²

2012

Class. Quantum Grav.

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“…Defining r = r + (α − 1)a, the line element takes the standard Minkowskian form. As we have mentioned before, from the Israel matching conditions for the metric tensors corresponding to (1) and ( 59), we find the singular contribution for the scalar curvature located at the bounding surface r = a [18]:…”

Section: Flower-pot Modelsupporting

confidence: 55%

“…First we shall consider the case where the charge is outside the monopole's core. Substituting ( 27) into (18) we see that Green's function is expressed in terms of two contributions:…”

Section: Green's Functionmentioning

confidence: 99%

“…Also for the cosmic string there is no closed expression for the metric tensor in the region inside; however, in the literature there are two different models proposed to describe the geometry inside the core: the ballpoint-pen model proposed independently by Gott and Hiscock [13] and flower-pot model [14]. Adopting the latter model for a global monopole, the calculations of vacuum polarization effects associated with massive scalar and fermionic fields have been developed in [18,19], respectively. Moreover, the analysis of electrostatic self-energies associated with electric charged particles placed at the rest in the global monopole spacetime considering both different models, have been calculated in [16,17].…”

Section: Applicationsmentioning

confidence: 99%

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

Barbosa

Freitas

Mello

2011

Class. Quantum Grav.

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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 threedimensional 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.Although the geometric properties of the spacetime outside the monopole are very well understood, there are no explicit expressions for the components of the metric tensor in the region inside. 1 As a consequence of this fact, many interesting investigations of physical effects associated with global monopole consider this object as a point-like defect. Adopting this simple model, calculations of vacuum polarization effects associated with bosonic [6] and fermionic quantum fields [7], in four-dimensional global monopole spacetime, present divergence on the monopole's core. Moreover, considering higher-dimensional spacetime, vacuum polarization effects associated with bosonic [8] and fermionic [9] quantum fields, also present divergences on the monopole's core.A very well known phenomenon that occur with an electric charged test particle placed at rest in a curved spacetime, is that it may become subjected to an electrostatic self-interactions. The origin of this induced self-interaction resides on the non-local structure of the field caused by the spacetime curvature and/or non-trivial topology. This phenomenon has been analyzed in an idealized cosmic string spacetime by Linet [10] and Smith [11], independently, and also in the spacetime of a global monopole considered as a point-like defect in [12]. In these analysis, the corresponding self-forces are repulsive and depend on the square of electric charge; moreover they present divergences on the respective defects' core. A possible way to circumvent the divergence problem is to consider these defects as having a non-vanishing radius, and attributing for the region inside a structure. For the cosmic string, two different models have been adopted to describe the geometry inside it: the ballpoint-pen model proposed independently by Gott and Hiscock [13], replaces the conical singularity at the string axis by a constant curvature spacetime in...

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Casimir Effect in Hemisphere Capped Tubes

Mello

Saharian

2015

Int J Theor Phys

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In this paper we investigate the vacuum densities for a massive scalar field with general curvature coupling in background of a (2+1)-dimensional spacetime corresponding to a cylindrical tube with a hemispherical cap. A complete set of mode functions is constructed and the positive-frequency Wightman function is evaluated for both the cylindrical and hemispherical subspaces. On the base of this, the vacuum expectation values of the field squared and energy-momentum tensor are investigated. The mean field squared and the normal stress are finite on the boundary separating two subspaces, whereas the energy density and the parallel stress diverge as the inverse power of the distance from the boundary. For a conformally coupled field, the vacuum energy density is negative on the cylindrical part of the space. On the hemisphere, it is negative near the top and positive close to the boundary. In the case of minimal coupling the energy density on the cup is negative. On the tube it is positive near the boundary and negative at large distances. Though the geometries of the subspaces are different, the Casimir pressures on the separate sides of the boundary are equal and the net Casimir force vanishes. The results obtained may be applied to capped carbon nanotubes described by an effective field theory in the long-wavelength approximation.

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Vacuum polarization by a global monopole with finite core

Cited by 16 publications

References 22 publications

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

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

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

Casimir Effect in Hemisphere Capped Tubes

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