Electromagnetic Casimir densities for planar boundaries in AdS spacetime

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040029 ◽  
Author(s):  
A. A. Saharian ◽  
A. S. Kotanjyan ◽  
A. A. Saharyan ◽  
H. G. Sargsyan
Keyword(s):  
Boundary Condition ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Curvature Radius ◽  
Perfect Conductor ◽  
Parallel Plates ◽  
Casimir Forces ◽  
Spatial Dimensions ◽  
Ads Spacetime

We investigate the vacuum expectation value of the energy-momentum tensor and the Casimir forces for the electromagnetic field in AdS spacetime for the geometry of two parallel plates. On the plates the field obeys the boundary condition that generalizes the perfect conductor boundary condition for an arbitrary number of spatial dimensions. The interaction forces between the plates are attractive. At separations larger than the curvature radius of the spacetime they decay exponentially.

scholarly journals Quantum Vacuum Effects in Braneworlds on AdS Bulk

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 181
Author(s):  
Aram A. Saharian
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Normal Component ◽  
Momentum Tensor ◽  
Dirac Field ◽  
Curvature Radius ◽  
Perfect Conductor ◽  
Quantum Vacuum ◽  
Local Properties

We review the results of investigations for brane-induced effects on the local properties of quantum vacuum in background of AdS spacetime. Two geometries are considered: a brane parallel to the AdS boundary and a brane intersecting the AdS boundary. For both cases, the contribution in the vacuum expectation value (VEV) of the energy–momentum tensor is separated explicitly and its behavior in various asymptotic regions of the parameters is studied. It is shown that the influence of the gravitational field on the local properties of the quantum vacuum is essential at distance from the brane larger than the AdS curvature radius. In the geometry with a brane parallel to the AdS boundary, the VEV of the energy–momentum tensor is considered for scalar field with the Robin boundary condition, for Dirac field with the bag boundary condition and for the electromagnetic field. In the latter case, two types of boundary conditions are discussed. The first one is a generalization of the perfect conductor boundary condition and the second one corresponds to the confining boundary condition used in QCD for gluons. For the geometry of a brane intersecting the AdS boundary, the case of a scalar field is considered. The corresponding energy–momentum tensor, apart from the diagonal components, has nonzero off-diagonal component. As a consequence of the latter, in addition to the normal component, the Casimir force acquires a component parallel to the brane.

scholarly journals Electromagnetic Casimir densities for a cylindrical shell on de Sitter space

2016 ◽  
Vol 31 (34) ◽  
pp. 1650183 ◽  
Author(s):  
A. A. Saharian ◽  
V. F. Manukyan ◽  
N. A. Saharyan
Keyword(s):  
Cylindrical Shell ◽  
Electric Field ◽  
Energy Momentum Tensor ◽  
Vacuum Expectation ◽  
Vacuum State ◽  
Momentum Tensor ◽  
Curvature Radius ◽  
Perfect Conductor ◽  
De Sitter ◽  
Proper Distance

Complete set of cylindrical modes is constructed for the electromagnetic field inside and outside a cylindrical shell in the background of [Formula: see text]-dimensional dS space–time. On the shell, the field obeys the generalized perfect conductor boundary condition. For the Bunch–Davies vacuum state, we evaluate the vacuum expectation values (VEVs) of the electric field squared and of the energy–momentum tensor. The shell-induced contributions are explicitly extracted. In this way, for points away from the shell, the renormalization is reduced to the one for the VEVs in the boundary-free dS bulk. As a special case, the VEVs are obtained for a cylindrical shell in the [Formula: see text]-dimensional Minkowski bulk. We show that the shell-induced contribution in the electric field squared is positive for both the interior and exterior regions. The corresponding Casimir–Polder forces are directed toward the shell. The vacuum energy–momentum tensor, in addition to the diagonal components, has a nonzero off-diagonal component corresponding to the energy flux along the direction normal to the shell. This flux is directed from the shell in both the exterior and interior regions. For points near the shell, the leading terms in the asymptotic expansions for the electric field squared and diagonal components of the energy–momentum tensor are obtained from the corresponding expressions in the Minkowski bulk replacing the distance from the shell by the proper distance in the dS bulk. The influence of the gravitational field on the local characteristics of the vacuum is essential at distances from the shell larger than the dS curvature radius. The results are extended for confining boundary conditions of flux tube models in QCD.

scholarly journals Electromagnetic Vacuum Densities Induced by a Cosmic String

Particles ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 13 ◽  
Author(s):  
Aram Saharian ◽  
Vardan Manukyan ◽  
Nvard Saharyan
Keyword(s):  
Cosmic String ◽  
Vacuum Expectation ◽  
Momentum Tensor ◽  
Curvature Radius ◽  
De Sitter ◽  
Dimensional Spacetime ◽  
Special Cases ◽  
Electric And Magnetic Fields ◽  
Spatial Dimensions ◽  
Planar Angle

We investigate the influence of a generalized cosmic string in (D+1)-dimensional spacetime on the local characteristics of the electromagnetic vacuum. Two special cases are considered with flat and locally de Sitter background geometries. The topological contributions in the vacuum expectation values (VEVs) of the squared electric and magnetic fields are explicitly separated. Depending on the number of spatial dimensions and on the planar angle deficit induced by the cosmic string, these contributions can be either negative or positive. In the case of the flat bulk, the VEV of the energy–momentum tensor is evaluated as well. For the locally de Sitter bulk, the influence of the background gravitational field essentially changes the behavior of the vacuum densities at distances from the string larger than the curvature radius of the spacetime.

scholarly journals CASIMIR EFFECT IN DE SITTER SPACETIME

2011 ◽  
Vol 03 ◽  
pp. 215-226 ◽  
Author(s):  
A. A. SAHARIAN
Keyword(s):  
Energy Momentum Tensor ◽  
Coupling Parameter ◽  
Momentum Tensor ◽  
Curvature Radius ◽  
De Sitter Spacetime ◽  
Parallel Plates ◽  
De Sitter ◽  
Casimir Forces ◽  
Massive Scalar Field ◽  
Sitter Spacetime

The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch–Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background spacetime decisively influences the behavior of the Casimir forces at separations larger than the curvature radius of de Sitter spacetime. In dependence of the curvature coupling parameter and the mass of the field, two different regimes are realized, which exhibit monotonic or oscillatory behavior of the forces. The decay of the Casimir force at large plate separation is shown to be power-law, with independence of the value of the field mass.

scholarly journals Fermionic vacuum polarization around a cosmic string in compactified AdS spacetime

2022 ◽  
Vol 2022 (01) ◽  
pp. 010
Author(s):  
S. Bellucci ◽  
W. Oliveira dos Santos ◽  
E.R. Bezerra de Mello ◽  
A.A. Saharian
Keyword(s):  
Energy Density ◽  
Cosmic String ◽  
Vacuum Energy ◽  
Energy Momentum Tensor ◽  
Minkowski Spacetime ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Vacuum Energy Density ◽  
Ads Spacetime

Abstract We investigate topological effects of a cosmic string and compactification of a spatial dimension on the vacuum expectation value (VEV) of the energy-momentum tensor for a fermionic field in (4+1)-dimensional locally AdS spacetime. The contribution induced by the compactification is explicitly extracted by using the Abel-Plana summation formula. The mean energy-momentum tensor is diagonal and the vacuum stresses along the direction perpendicular to the AdS boundary and along the cosmic string are equal to the energy density. All the components are even periodic functions of the magnetic fluxes inside the string core and enclosed by compact dimension, with the period equal to the flux quantum. The vacuum energy density can be either positive or negative, depending on the values of the parameters and the distance from the string. The topological contributions in the VEV of the energy-momentum tensor vanish on the AdS boundary. Near the string the effects of compactification and gravitational field are weak and the leading term in the asymptotic expansion coincides with the corresponding VEV in (4+1)-dimensional Minkowski spacetime. At large distances, the decay of the cosmic string induced contribution in the vacuum energy-momentum tensor, as a function of the proper distance from the string, follows a power law. For a cosmic string in the Minkowski bulk and for massive fields the corresponding fall off is exponential. Within the framework of the AdS/CFT correspondence, the geometry for conformal field theory on the AdS boundary corresponds to the standard cosmic string in (3+1)-dimensional Minkowski spacetime compactified along its axis.

scholarly journals CASIMIR EFFECT IN DE SITTER SPACETIME

2011 ◽  
Vol 26 (22) ◽  
pp. 3833-3844 ◽  
Author(s):  
A. A. SAHARIAN
Keyword(s):  
Energy Momentum Tensor ◽  
Coupling Parameter ◽  
Momentum Tensor ◽  
Curvature Radius ◽  
De Sitter Spacetime ◽  
Parallel Plates ◽  
De Sitter ◽  
Casimir Forces ◽  
Massive Scalar Field ◽  
Sitter Spacetime

The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch–Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background space-time decisively influences the behavior of the Casimir forces at separations larger than the curvature radius of de Sitter spacetime. In dependence of the curvature coupling parameter and the mass of the field, two different regimes are realized, which exhibit monotonic or oscillatory behavior of the forces. The decay of the Casimir force at large plate separation is shown to be power-law, with independence of the value of the field mass.

scholarly journals Fermionic condensate and the Casimir effect in cosmic string spacetime

2017 ◽  
Vol 26 (07) ◽  
pp. 1750064 ◽  
Author(s):  
A. Kh. Grigoryan ◽  
A. R. Mkrtchyan ◽  
A. A. Saharian
Keyword(s):  
Energy Density ◽  
Cosmic String ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Vacuum Energy Density ◽  
Casimir Forces ◽  
Massless Field

We investigate combined effects of nontrivial topology, induced by a cosmic string, and boundaries on the fermionic condensate and the vacuum expectation value (VEV) of the energy–momentum tensor for a massive fermionic field. As geometry of boundaries we consider two plates perpendicular to the string axis on which the field is constrained by the MIT bag boundary condition. By using the Abel–Plana type summation formula, the VEVs in the region between the plates are decomposed into the boundary-free and boundary-induced contributions for general case of the planar angle deficit. The boundary-induced parts in both the fermionic condensate and the energy–momentum tensor vanish on the cosmic string. Fermionic condensate is positive near the string and negative at large distances, whereas the vacuum energy density is negative everywhere. The radial stress is equal to the energy density. For a massless field, the boundary-induced contribution in the VEV of the energy–momentum tensor is different from zero in the region between the plates only and it does not depend on the coordinate along the string axis. In the region between the plates and at large distances from the string, the decay of the topological part is exponential for both massive and massless fields. This behavior is in contrast to that for the VEV of the energy–momentum tensor in the boundary-free geometry with the power law decay for a massless field. The vacuum pressure on the plates is inhomogeneous and vanishes at the location of the string. The corresponding Casimir forces are attractive.

Vacuum polarization in the background of conical singularity

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040030
Author(s):  
Yuri V. Grats ◽  
Pavel Spirin
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Energy Momentum Tensor ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Dimensional Spacetime ◽  
Higher Dimensional

We consider the gravity-induced effects associated with a massless scalar field living in a higher-dimensional spacetime being the tensor product of Minkowski space and spherically-symmetric space with angle deficit. These spacetimes are considered as simple models for a multidimensional global monopole or cosmic string with flat extra dimensions, where the deficit of solid angle is proportional to Newton constant and tension. Thus, we refer to them as conical backgrounds. In terms of the angular deficit value, we derive the perturbative expression for the scalar Green’s function and compute it to the leading order. With the use of this Green’s function we compute the renormalized vacuum expectation value of the scalar-field’s energy-momentum tensor. We make some general note on the linear-on-curvature part of the trace of even coefficients of Schwinger-deWitt expansion.

scholarly journals Effects of Quantum Fields Outside Cosmic Strings

1988 ◽  
Vol 130 ◽  
pp. 565-565
Author(s):  
D. A. Konkowski ◽  
T. M. Helliwell
Keyword(s):  
Cosmic String ◽  
Casimir Effect ◽  
Semiclassical Approximation ◽  
Mass Density ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Energy Tensor ◽  
Parallel Plates ◽  
Vacuum Fluctuations ◽  
Gravitational Influence

The space surrounding a long straight cosmic string is flat but conical. The conical topology implies that such a string focuses light rays or particles passing by opposite sides of the string, which can have important astrophysical effects. The flatness, however, implies that the string has no gravitational influence on matter at rest with respect to the string. The flatness is a consequence of the fact that the tension along a cosmic string is equal to its linear mass density μ. There may be physical effects, however, which destroy the equality of tension and mass density, so that straight strings might after all affect matter at rest. One such effect we and others have calculated is the vacuum fluctuations of fields near the strings induced by the conical topology. Such fluctuation s are physically observable but normally small, as in the Casimir effect between parallel plates. We find the vacuum expectation value of the stress - energy tensor of a conformally coupled scalar field around a cosmic string to be in cylindrical coordinates (t, r, θ, z). The equality of Ttt and Tzz means that the effective tension and mass density of the vacuum fluctuations are equal, so that at least in a semiclassical approximation a string dressed by such fields still has no gravitational influence on matter at rest, even though it has a substantial mass density.

scholarly journals Thermal Condensate Structure and Cosmological Energy Density of the Universe

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Antonio Capolupo ◽  
Gaetano Lambiase ◽  
Giuseppe Vitiello
Keyword(s):  
Energy Density ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Microwave Background ◽  
Thermal Vacuum ◽  
Fermion Fields ◽  
Formal Framework ◽  
The Universe ◽  
Thermal States

The aim of this paper is to study thermal vacuum condensate for scalar and fermion fields. We analyze the thermal states at the temperature of the cosmic microwave background (CMB) and we show that the vacuum expectation value of the energy momentum tensor density of photon fields reproduces the energy density and pressure of the CMB. We perform the computations in the formal framework of the Thermo Field Dynamics. We also consider the case of neutrinos and thermal states at the temperature of the neutrino cosmic background. Consistency with the estimated lower bound of the sum of the active neutrino masses is verified. In the boson sector, nontrivial contribution to the energy of the universe is given by particles of masses of the order of 10−4 eV compatible with the ones of the axion-like particles. The fractal self-similar structure of the thermal radiation is also discussed and related to the coherent structure of the thermal vacuum.

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